Re-generation and re-transmission of millimeter waves for building penetration

ABSTRACT

A system for enabling signal penetration into a building includes first circuitry, located on an outside of the building, that receives millimeter wave signals and converting the millimeter wave signals into a format that penetrates into an interior of a building for reception by wireless devices within the building. Second circuitry, located on an inside of the building and communicatively linked with the first circuitry, receives the millimeter wave signals in the format that penetrates into an interior of the building and converts the millimeter wave signals in the format to a second format for transmission to the wireless devices within the building.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims benefit of U.S. Provisional Application No.62/317,829, filed Apr. 4, 2016, entitled RE-GENERATION ANDRE-TRANSMISSION OF MILLIMETER WAVES FOR BUILDING PENETRATION, and claimsbenefit of U.S. Provisional Application No. 62/321,245, filed Apr. 12,2016, entitled RE-GENERATION AND RE-TRANSMISSION OF MILLIMETER WAVES FORBUILDING PENETRATION, and claims benefit of U.S. Provisional ApplicationNo. 62/368,417, filed Jul. 29, 2016, entitled REGENERATION,RETRANSMISSION OF MILLIMETER WAVES FOR INDOOR PENETRATION, and claimsbenefit of U.S. Provisional Application No. 62/369,393, filed Aug. 1,2016, entitled REGENERATION, RETRANSMISSION OF MILLIMETER WAVES FORINDOOR PENETRATION, and U.S. Provisional Application No. 62/425,432,filed Nov. 22, 2016, entitled REGENERATION, RETRANSMISSION OF MILLIMETERWAVES FOR BUILDING PENETRATION USING HORN ANTENNAS. U.S. ApplicationNos. 62/317,829, 62/321,245, 62/368,417, 62/369,393 and 62/425,432 areincorporated by reference herein in their entirety.

This application is a continuation-in-part of U.S. application Ser. No.15/357,808, filed on Nov. 21, 2016, entitled SYSTEM AND METHOD FORCOMMUNICATION USING ORBITAL ANGULAR MOMENTUM WITH MULTIPLE LAYER OVERLAYMODULATION, which is a continuation of U.S. patent application Ser. No.15/144,297, filed on May 2, 2016, entitled SYSTEM AND METHOD FORCOMMUNICATION USING ORBITAL ANGULAR MOMENTUM WITH MULTIPLE LAYER OVERLAYMODULATION, now U.S. Pat. No. 9,503,258, issued on Nov. 22, 2016. U.S.application Ser. No. 15/144,297 is a continuation of U.S. applicationSer. No. 14/323,082, filed on Jul. 3, 2014, entitled SYSTEM AND METHODFOR COMMUNICATION USING ORBITAL ANGULAR MOMENTUM WITH MULTIPLE LAYEROVERLAY MODULATION, now U.S. Pat. No. 9,331,875, issued on May 3, 2016,which claims benefit of U.S. Provisional Application No. 61/975,142,filed Apr. 4, 2014, entitled SYSTEM AND METHOD FOR COMMUNICATION USINGORBITAL ANGULAR MOMENTUM WITH MODULATION. U.S. application Ser. Nos.15/357,808, 15/144,297, 14/323,082, and 61/975,142, and U.S. Pat. Nos.9,503,258 and 9,331,875 are incorporated by reference herein in theirentirety.

TECHNICAL FIELD

The present invention relates to millimeter wave transmissions, and moreparticularly, to a manner for improving building penetration formillimeter wave transmissions.

BACKGROUND

Millimeter wave transmissions were developed as a bandwidth plan formaking 1300 MHz of the local multipoint distribution service (LMDS)spectrum available within the United States. The millimeter wavetransmissions meet the needs for increased bandwidth availability due tothe increasing bandwidth and application requirements for wirelessmobile devices. However, while increasing bandwidth capabilities,millimeter wave transmissions have the problem of having very poorbuilding penetration capabilities. Signals are drastically degraded whenattempting to penetrate most building structures. This provides aserious problem since the vast majority of wireless signaling traffic isoriginated from within buildings and the inability to utilize millimeterwave bandwidths would drastically limit its implementation in the modernmarketplace. Thus, there is a need for some manner for improvingbuilding penetration characteristics of millimeter wave transmissions.

SUMMARY

The present invention, as disclosed and described herein, in one aspectthereof comprises a system for enabling signal penetration into abuilding includes first circuitry, located on an outside of thebuilding, that receives millimeter wave signals and converting themillimeter wave signals into a format that penetrates into an interiorof a building for reception by wireless devices within the building.Second circuitry, located on an inside of the building andcommunicatively linked with the first circuitry, receives the millimeterwave signals in the format that penetrates into an interior of thebuilding and converts the millimeter wave signals in the format to asecond format for transmission to the wireless devices within thebuilding.

BRIEF DESCRIPTION OF THE DRAWINGS

For a more complete understanding, reference is now made to thefollowing description taken in conjunction with the accompanyingDrawings in which:

FIG. 1 illustrates millimeter wave transmissions between a base stationand receivers located both inside and outside of a building structure;

FIG. 2A illustrates a block diagram of an optical bridge fortransmitting millimeter wave transmissions through a window;

FIG. 2B illustrates a block diagram of an embodiment wherein receivedsignals are down converted to a level that more easily transmits througha window or wall;

FIG. 3 is a more detailed block diagram of the millimeter waveregeneration and retransmission circuitry;

FIG. 4 illustrates the misalignment losses associated with themillimeter wave regeneration and retransmission circuitry;

FIG. 5 illustrates the RF transceiver circuitry of the millimeter waveregeneration and retransmission circuitry;

FIG. 6 illustrates the optical focusing circuitry of the millimeter waveregeneration and retransmission circuitry;

FIG. 7 illustrates various techniques for increasing spectral efficiencywithin a transmitted signal;

FIG. 8 illustrates a particular technique for increasing spectralefficiency within a transmitted signal;

FIG. 9 illustrates a general overview of the manner for providingcommunication bandwidth between various communication protocolinterfaces;

FIG. 10 illustrates the manner for utilizing multiple level overlaymodulation with twisted pair/cable interfaces;

FIG. 11 illustrates a general block diagram for processing a pluralityof data streams within an optical communication system;

FIG. 12 is a functional block diagram of a system for generating orbitalangular momentum within a communication system;

FIG. 13 is a functional block diagram of the orbital angular momentumsignal processing block of FIG. 6;

FIG. 14 is a functional block diagram illustrating the manner forremoving orbital angular momentum from a received signal including aplurality of data streams;

FIG. 15 illustrates a single wavelength having two quanti-spinpolarizations providing an infinite number of signals having variousorbital angular momentums associated therewith;

FIG. 16A illustrates a plane wave having only variations in the spinangular momentum;

FIG. 16B illustrates a signal having both spin and orbital angularmomentum applied thereto;

FIGS. 17A-17C illustrate various signals having different orbitalangular momentum applied thereto;

FIG. 17D illustrates a propagation of Poynting vectors for various Eigenmodes;

FIG. 17E illustrates a spiral phase plate;

FIG. 18 illustrates a multiple level overlay modulation system;

FIG. 19 illustrates a multiple level overlay demodulator;

FIG. 20 illustrates a multiple level overlay transmitter system;

FIG. 21 illustrates a multiple level overlay receiver system;

FIGS. 22A-22K illustrate representative multiple level overlay signalsand their respective spectral power densities;

FIG. 23 illustrates comparisons of multiple level overlay signals withinthe time and frequency domain;

FIG. 24 illustrates a spectral alignment of multiple level overlaysignals for differing bandwidths of signals;

FIG. 25 illustrates an alternative spectral alignment of multiple leveloverlay signals;

FIG. 26 illustrates power spectral density for various signal layersusing a combined three layer multiple level overlay technique;

FIG. 27 illustrates power spectral density on a log scale for layersusing a combined three layer multiple level overlay modulation;

FIG. 28 illustrates a bandwidth efficiency comparison for square rootraised cosine versus multiple layer overlay for a symbol rate of 1/6;

FIG. 29 illustrates a bandwidth efficiency comparison between squareroot raised cosine and multiple layer overlay for a symbol rate of 1/4;

FIG. 30 illustrates a performance comparison between square root raisedcosine and multiple level overlay using ACLR;

FIG. 31 illustrates a performance comparison between square root raisedcosine and multiple lever overlay using out of band power;

FIG. 32 illustrates a performance comparison between square root raisedcosine and multiple lever overlay using band edge PSD;

FIG. 33 is a block diagram of a transmitter subsystem for use withmultiple level overlay;

FIG. 34 is a block diagram of a receiver subsystem using multiple leveloverlay;

FIG. 35 illustrates an equivalent discreet time orthogonal channel ofmodified multiple level overlay;

FIG. 36 illustrates the PSDs of multiple layer overlay, modifiedmultiple layer overlay and square root raised cosine;

FIG. 37 illustrates a bandwidth comparison based on −40 dBc out of bandpower bandwidth between multiple layer overlay and square root raisedcosine;

FIG. 38 illustrates equivalent discrete time parallel orthogonalchannels of modified multiple layer overlay;

FIG. 39 illustrates the channel power gain of the parallel orthogonalchannels of modified multiple layer overlay with three layers andT_(sym)=3;

FIG. 40 illustrates a spectral efficiency comparison based on ACLR1between modified multiple layer overlay and square root raised cosine;

FIG. 41 illustrates a spectral efficiency comparison between modifiedmultiple layer overlay and square root raised cosine based on OBP;

FIG. 42 illustrates a spectral efficiency comparison based on ACLR1between modified multiple layer overlay and square root raised cosine;

FIG. 43 illustrates a spectral efficiency comparison based on OBPbetween modified multiple layer overlay and square root raised cosine;

FIG. 44 illustrates a block diagram of a baseband transmitter for a lowpass equivalent modified multiple layer overlay system;

FIG. 45 illustrates a block diagram of a baseband receiver for a lowpass equivalent modified multiple layer overlay system;

FIG. 46 illustrates a free-space communication system;

FIG. 47 illustrates a block diagram of a free-space optics system usingorbital angular momentum and multi-level overlay modulation;

FIGS. 48A-48C illustrate the manner for multiplexing multiple datachannels into optical links to achieve higher data capacity;

FIG. 48D illustrates groups of concentric rings for a wavelength havingmultiple OAM valves;

FIG. 49 illustrates a WDM channel containing many orthogonal OAM beams;

FIG. 50 illustrates a node of a free-space optical system;

FIG. 51 illustrates a network of nodes within a free-space opticalsystem;

FIG. 52 illustrates a system for multiplexing between a free spacesignal and an RF signal;

FIG. 53 illustrates alignment holes within a VCSEL;

FIG. 54 illustrates the use of alignment holes for aligning opticalcircuits of VCSELs;

FIG. 55 illustrates optical power coupling between VCSELs;

FIG. 56 illustrates an embodiment using horn antennas for transmittingdata through a window or wall;

FIG. 57 illustrates a downlink losses in the embodiment of FIG. 56;

FIG. 58 illustrates up link signal strengths in the embodiment of FIG.56;

FIG. 59 illustrates up link signal strengths when a power amplifier islocated inside of the building in the embodiment of FIG. 56;

FIG. 60 illustrates gains and losses on a downlink of the embodiment ofFIG. 59 when no power amplifier is incorporated;

FIG. 61 illustrates signal strengths at various points of the uplinkwhen no power amplifier is provided in the embodiment of FIG. 56;

FIG. 62 illustrates shielding used incorporation with the embodiment ofFIG. 56;

FIG. 63 illustrates a manner for powering external system componentsusing solar panels;

FIG. 64 illustrates a manner for powering external system componentsusing lasers; and

FIG. 65 illustrates a manner for powering exterior components from aninterior power source using inductive coupling.

DETAILED DESCRIPTION

Referring now to the drawings, wherein like reference numbers are usedherein to designate like elements throughout, the various views andembodiments of regeneration and retransmission of millimeter waves forbuilding penetration are illustrated and described, and other possibleembodiments are described. The figures are not necessarily drawn toscale, and in some instances the drawings have been exaggerated and/orsimplified in places for illustrative purposes only. One of ordinaryskill in the art will appreciate the many possible applications andvariations based on the following examples of possible embodiments.

Millimeter wave signaling was developed when the FCC devised a band planmaking 1300 MHz of local multipoint distribution service (LMDS) spectrumavailable within each basic trading area across the United States. Theplan allocated two LMDS licenses per BTA (basic trading area), an “ABlock” and a “B Block” in each. The A Block license comprised 1150 MHzof total bandwidth, and the B Block license consisted of 150 MHz oftotal bandwidth. A license holder Teligent developed a system for fixedwireless point to multipoint technology that could send high speedbroadband from rooftops to surrounding small and medium-size businesses.However, the system, as well as others provided by Winstar and NextLink,did not succeed and many of the LMDS licenses fell back into the handsof the FCC. These licenses and related spectrum are seen as useful for5G trials and services.

Referring now to the drawings, and more particularly to FIG. 1, there isillustrated the use of a millimeter wave transmission system 102 forcommunications. The base station 104 generates the millimeter wavetransmissions 106, 108 for transmissions to various receivers 110, 112.Millimeter wave transmissions 106 that traveled directly from the basestation 104 to a receiver 110 are able to be easily received withoutmuch ambient interference. Millimeter wave transmissions 108 from a basestation 104 to a receiver 112 located inside of the building 114 willhave significant interference issues. Millimeter wave transmissions 108do not easily penetrate a building 104. When passing through transparentwindows or building walls significant signal losses are experienced. The28 GHz and above frequencies do not penetrate building walls and glassof the windows yet 85% of communications traffic is generated fromwithin buildings.

In view of millimeter wave spectrum transmissions not propagating veryfar and lacking the ability to penetrate indoors, these frequencies willbe used for very short range applications of about a mile. By way ofperspective, at 2.4 GHz, a low-power Wi-Fi can cover most of a housethat's under 3000 sq. ft., but a 5 GHz Wi-Fi signal would only coverapproximately 60% of a two-story house because the signal does nottravel as far at the higher frequency range. For 5G applications, thepower is higher, but still higher frequencies have higher losses andpropagation through space and other media.

The losses occurring as the millimeter wave signals penetrate a buildingdrive data rates down to almost nothing. For example, when transmittingon a downlink from a base station to the inside of a home or buildingthrough clear glass, the maximum data rate is 9.93 Gb per second. Whentransmitting through tinted glass the data rate is 2.2 Mb per second.When transmitting through brick the data rate is 14 Mb per second, andwhen transmitting through concrete, the data rate drops all the way to0.018 bps. Similarly, when transmitting on an uplink from the inside ofthe building towards a base station, the maximum data rate through clearglass is 1.57 Gb per second and through tinted glass is 0.37 Mb persecond. The signal being transmitted on the uplink has a data rate of5.5 Mb per second when transmitted through brick and 0.0075 bits persecond when transmitted through concrete. Differences are also providedon the downlink and uplink when transmitting to/from older or newerbuildings. Older buildings are defined as buildings using a compositemodel that comprises 30% standard glass and 70% concrete wall. Newerbuildings are defined as composite models comprising 70% infraredreflective glass (IRR glass) and 30% concrete wall. Base stationtransmissions on the downlink to the inside of the building are 32 Mbper second for older buildings and 0.32 Mb per second for newerbuildings. Similarly, the uplink transmissions from inside thehome/building to the base station are 2.56 Mb per second for olderbuildings in 25.6 kb per second for newer buildings.

Despite the shortcomings, in order to meet the increased demands forbandwidth, RF service providers will increasingly move to carrierfrequencies of higher frequency rates. In particular, 28 GHz is anemerging frequency band for providing local multipoint distributionservice (LMDS). The 28 GHz and 39 GHz frequency bands are beingcontemplated by the FCC for small cell deployments to support 5Gnetworks to subscriber premises using beam forming and beam steering.These higher frequency bandwidths have a number of advantages inaddition to the disadvantages caused by the huge penetration losses whenpassing through building materials or windows. These advantages includea higher frequency rate, capability of more precise beamforming and moreeffective beam steering in the smaller footprint of the componentsproviding the millimeter wave frequencies.

FIG. 2A illustrates one manner for transmitting millimeter wave signalsinside of a building using an optical bridge 202 mounted to a window204. The optical bridge 202 includes a first portion 206 included on anoutside of the window 204 and a second portion 208 included on theinside of the window 204. The first portion 206 includes a 28 GHztransceiver 210 that is mounted on the outside of the window 204. The 28GHz transceiver 210 receives the millimeter wave transmissions that arebeing transmitted from, for example, a base station 104 such as thatdescribed with respect to FIG. 1. The received/transmitted signals aretransmitted to and from the transceiver 210 using a receiver opticalsubassembly (ROSA)/transmission optical subassembly (TOSA) 212. Areceiver optical subassembly is a component used for receiving opticalsignals in a fiber optic system. Similarly, a transceiver opticalsubassembly is a component used for transmitting optical signals in afiber optic system. ROSA/TOSA component 212 transmits or receives theoptical signals through the window 204 to a ROSA/TOSA component 214located on the inside of the window 204. The signals are forwarded fromthe ROSA/TOSA 214 to a Wi-Fi transmitter 216 for transmissions withinthe building.

FIG. 2B illustrates a further embodiment wherein a received frequencythat does not easily penetrate a tinted window or wall 230 down convertsa received signal in order to facilitate transmission between the windowor wall 230. On the exterior of the building, a signal is received at anantenna 232 of a transceiver 234 at a frequency that does not easilypenetrate a window or wall. The transceiver 234 forwards the signals toa down/up converter 236 for down converting the signals to a frequencyband that will more easily penetrate the window/wall 230. Anothertransceiver 238 takes the frequency down converted signal from theconverter 236 and transmits it through the wall or window 230. Thetransmitted signal is received by a transceiver 240 located on theinterior of the building at the down converted frequency. The receivedsignal is passed to an up/down converter 242 to convert the signal to alevel for transmission in the interior of the building. In many casesthis may be the Wi-Fi band. The up converted signal is forwarded to arouter 244 for transmission within the building. Outgoing signalreceived from devices located within the building are processed andtransmitted in a reverse manner to transmit the signal outside of thebuilding from transceiver 234.

Referring now to FIG. 3, there is illustrated a more detailedillustration of the components for transmitting millimeter wavetransmissions through a window or wall of a building. The transceiver210 includes an optional antenna gain element 302 for receiving themillimeter wave transmissions transmitted on a down/up link 304 from abase station 104. The down/uplink 304 comprises a 28 GHz beamtransmission. However other frequency transmissions may also beutilized. An RF receiver 306 is used for receiving information from thebase station 104 over the down/up link 304. Similarly, the RFtransmitter 308 is used for transmitting information on the down/up link304 to a base station 104. Receive signals are provided to a demodulator310 for demodulation of any received signals. The demodulated signalsare provided to a groomer 312 which places the signals in theappropriate configuration for transmission by the optical transmissioncomponents. When translating different modulations (say from a highorder QAM to OOK (On-Off Keying)), there are signaling conversions thatrequire some grooming (or signal conditioning) to ensure all bitstranslate properly and still provide a low BER. The present systemtranslates from RF at a high QAM rate to raw bit rates of OOK to enabletransmissions using the VCSELs to go through the glass of the window.VCSELs only work with OOK and therefore a translation using the groomer312 is needed. If a received signal were just down-convert from 28 GHzdirectly to 5.8 GHz (because 5.8 GHz does pass through the wall andglass), then we do not need to worry about complications of translatingto low order modulation. The problem is that down-converting signal from28 GHz to 5.8 GHz requires expensive components. The groomer 312completes the translation of the received 28 GHz signal to a frequencyfor transmission through a glass or wall without the more expensivecomponents.

The signals to be transmitted are passed through an amplifier 314 toamplify the signal for transmission. The amplified signal is provided toVCSELs 316 for optically transmitting the signal. The VCSEL 316 is avertical cavity surface emitting laser that is a type of semiconductorlaser diode with laser beam omissions perpendicular from the topsurface. In a preferred embodiment, the VCSEL 316 comprises a FinisarVCSEL having a wavelength of approximately 780 nm, a modulation rate of4 Gb per second and an optical output power of 2.2 mW (3.4 to dBm). Inalternative embodiments the components for transmitting the opticalsignals across the window 204 may comprise an LED (light emitting diode)or EEL (edge emitting lasers). The different lasers enable differentoptical re-transmissions at different frequencies based on differentcharacteristics of a window such as tint.

The VCSEL 316 includes a transmission optical subassembly (TOSA) forgenerating the optical signals for transmission from VCSEL 316 to VCSEL318 located on the opposite side of the window 204. The VCSELs 316 and318 comprise a laser source for generating the optical signals fortransmission across the window 204. In one embodiment, the VCSELcomprises a Finisar VCSEL that provides a 780 nm optical signal having amaximum modulation rate of 4 Gb per second when running at 1 Gb persecond and an optical output power of 3 mW (5 dBm). The TOSA includes alaser device or LED device for converting electrical signals from theamplifier 314 into light signal transmissions. Transmissions from theoutside VCSEL 316 to the inside VCSEL 318 and an associated receiveroptical subassembly (ROSA).

The optical signals are transmitted through the window 204 using opticalfocusing circuitry 317. The optical focusing circuitry 317 will be morefully described on the transmitter and receiver sides with respect toFIG. 6. The optical link 328 between VCSEL 316 and VCSEL 318 has anoptical link budget associated therewith that defines the losses thatmay be accepted while still transmitting the information between theVCSELs 316, 318. The VCSEL has an output power of approximately 5 dBm.The detector at the receiver within the VCSEL can detect a signal atapproximately −12 dBm. The glass losses associated with the opticalsignal passing through the glass at a wavelength of 780 nm is 7.21 dB.The coupling loss and lens gain associated with the transmission isapproximately 0.1 dB. The maximum displacement loss caused by a lensdisplacement of 3.5 mm is 6.8 dB. Thus, the total link margin equals2.88 dB based upon a subtraction of the detector sensitivity, glasslosses, coupling loss and lens gain and maximum displacement loss fromthe VCSEL output power. The 2.88 dB link margin is provided forunexpected an extra losses such as len's losses and unexpected outputvariances.

Lens displacement or misalignment can account for a significant portionof the link loss within the system. As illustrated in FIG. 4, the rangeof tolerable misalignment 402 ranges from approximately −6.5 mm to +6.5mm from the center of the power spectrum received by the detector. Thealignment losses 404 range in an area from 0.6 dB to 6.8 dB as themisalignment moves between ±6.5 mm. The maximum allowed misalignmentloss is 9.4 dB as illustrated at 406.

The VCSEL 318 on the inside of the window 204 uses a TOSA to transmit anoptical signal at a data rate of 0.5 Gbps through the window 204 to aROSA within the VCSEL 316 located on the outside of the window. Thereceived optical signal is provided to a de-groomer component 32 forprocessing the signals from raw bit rates of OOK to RF at high QAM rateto enable RF transmissions after receipt of the signals by the VCSELs.The de-groomed signal is modulated within a modulator 322. The modulatedsignal is transmitted over the uplink 304 using an RF transmitter 308.The transceiver 210 is powered by a power input 324 the componentsinside the window are similarly powered by a power input 326. Signalsare provided within the building using a Wi-Fi transmitter 328 that isconnected to receive optical signals received by the VCSEL 318 andprovide signals to the VCSEL 318 for transmission through the window204. The Wi-Fi transmitter uses the 802.11 transmission protocol.

Referring now to FIG. 5 there is illustrated a more detailed blockdiagram of the transceiver 210. The receiver portion 502 includes an RFreceiver 504 for receiving the RF signals transmitted from the basestation on the downlink 506. The receiver 504 generates output signalshaving a real portion BBI 508 and an imaginary portion BBQ 510. The RFreceiver 504 generates the real signal 508 and imaginary signal 510responsive to the receive signal and inputs from a phase lockedloop/voltage control oscillator 505. The phase locked loop/voltagecontrol oscillator 505 provides inputs to the RF receiver 504 responsiveto a reference oscillator signal provided from reference oscillator 507and a voltage controlled oscillator signal provided from oscillator 509.The real signal 508 and the imaginary signal 510 are provided toanalog-to-digital converters 512 for conversion to a digital signal. Theanalog-to-digital converters 512 are clocked by an associated clockinput 514 provided from clock generation circuit 516. The clockgeneration circuit 516 also receives an input from the referenceoscillator 507. The real and imaginary digital signals 518 and 520 areinput to a digital down converter 522. The digital signals are downconverted to a lower frequency and output as a bit stream 524 to theoptical transmission circuitry (VCSEL) for transmitting across thewindow glass.

The transmitter portion 524 receives a digital bitstream 526 from theoptical circuitry and provides this bitstream to the real and imaginaryportions of digital up converters 528 to convert the digital data to ahigher frequency for transmission. The real and imaginary portions ofthe up-converted digital signal are provided to a crest factor reductionprocessor 530. Some signals (especially OFDM-based systems) have highpeak-to-average power ratio (PAR) that negatively impacts the efficiencyof power amplifiers (PAs). Crest factor reduction (CFR) schemesimplemented by the processor help reduce PAR and have been used for manynetworks (CDMA & OFDM). However, CFR schemes developed primarily forCDMA signals have a poor performance when used in OFDM (given the tighterror vector magnitude (EVM) requirements). With a well-designed CFRalgorithm on FPGAs, one can achieve low-latency, high-performance thatcan significantly reduce the PAR of the output signal which improves PAefficiency and reduced cost.

The real and imaginary signals are provided from the crest factorreduction processor 530 to a digital to analog converter 532. Thedigital to analog converter 532 converts the real and imaginary digitalsignals into real and imaginary analog signals BBI 534 and BBQ 536. Thereal and imaginary analog signals are inputs to the RF transmitter 538.The RF transmitter 538 processes the real signal 534 and imaginarysignal 536 responsive to input from the phase locked loop/voltagecontrol oscillator 504 to generate RF signals for transmission on theuplink 540 to generate the millimeter wave and transmissions.

Referring now to FIG. 6, there is illustrated the optical focusingcircuitry 317 associated with the optical transmission interface acrossthe window 204. The optical focusing circuitry 317 is included with theVCSEL located on each side of the window 204 and includes a transmissionportion 602 and a receiver portion 604. The transmission portion 602 andreceiver portion 604 would be included on each side of the window 204 asthe system provides bidirectional communications across the window. Thetransmission portion 602 includes in one embodiment a VCSEL 606 providedby Finisar that transmits a 780 nm optical signal at 4 Gb per second andhas a power output of 3.42 dBm. The optical signal generated by theVCSEL 606 is provided to an acromatic doublet 608 having a focal lengthof 7.5 mm that collimates the optical signal generated by the VCSEL 606into a small aperture. A collimated beam 610 is transmitted across thewindow 204. The collimated beam exits the window 204 and on the receiverportion 604 first passes through a bi-convex lens 612 having a focallength of 25 mm. The bi-convex lens 612 focuses the beam column 610 ontoa half ball lens 614 that focuses the optical signal onto asemiconductor aperture of a photo detector 616. In one embodiment, thedetector 616 has an aperture diameter of 10 mm and a detectorsensitivity of 12 dBm.

The transmissions between the VCSELs 606 and to and from the RFtransceiver to 10 may in one particular embodiment utilize orthogonalfunction signal transmission techniques such as those described in U.S.application Ser. No. 15/357,808, entitled SYSTEM AND METHOD FORCOMMUNICATION USING ORBITAL ANGULAR MOMENTUM WITH MULTIPLE LAYER OVERLAYMODULATION, filed on Nov. 21, 2016, which is incorporated herein byreference in its entirety. However, it should be realized that a varietyof other data transmission techniques may also be used.

FIG. 7 illustrates two manners for increasing spectral efficiency of acommunications system. In general, there are basically two ways toincrease spectral efficiency 702 of a communications system. Theincrease may be brought about by signal processing techniques 704 in themodulation scheme or using multiple access technique. Additionally, thespectral efficiency can be increase by creating new Eigen channels 706within the electromagnetic propagation. These two techniques arecompletely independent of one another and innovations from one class canbe added to innovations from the second class. Therefore, thecombination of this technique introduced a further innovation.

Spectral efficiency 702 is the key driver of the business model of acommunications system. The spectral efficiency is defined in units ofbit/sec/hz and the higher the spectral efficiency, the better thebusiness model. This is because spectral efficiency can translate to agreater number of users, higher throughput, higher quality or some ofeach within a communications system.

Regarding techniques using signal processing techniques or multipleaccess techniques. These techniques include innovations such as TDMA,FDMA, CDMA, EVDO, GSM, WCDMA, HSPA and the most recent OFDM techniquesused in 4G WIMAX and LTE. Almost all of these techniques use decades-oldmodulation techniques based on sinusoidal Eigen functions called QAMmodulation. Within the second class of techniques involving the creationof new Eigen channels 706, the innovations include diversity techniquesincluding space and polarization diversity as well as multipleinput/multiple output (MIMO) where uncorrelated radio paths createindependent Eigen channels and propagation of electromagnetic waves.

Referring now to FIG. 8, the communication system configurationintroduces two techniques, one from the signal processing techniques 704category and one from the creation of new eigen channels 706 categorythat are entirely independent from each other. Their combinationprovides a unique manner to disrupt the access part of an end to endcommunications system from twisted pair and cable to fiber optics, tofree space optics, to RF used in cellular, backhaul and satellite. Thefirst technique involves the use of a new signal processing techniqueusing new orthogonal signals to upgrade QAM modulation using nonsinusoidal functions. This particular embodiment is referred to asquantum level overlay (QLO) 802. The second embodiment involves theapplication of new electromagnetic wavefronts using a property ofelectromagnetic waves or photon, called orbital angular momentum (QAM)704. Application of each of the quantum level overlay techniques 802 andorbital angular momentum application 804 uniquely offers orders ofmagnitude higher spectral efficiency 806 within communication systems intheir combination.

With respect to the quantum level overlay technique 802, new eigenfunctions are introduced that when overlapped (on top of one anotherwithin a symbol) significantly increases the spectral efficiency of thesystem. The quantum level overlay technique 302 borrows from quantummechanics, special orthogonal signals that reduce the time bandwidthproduct and thereby increase the spectral efficiency of the channel.Each orthogonal signal is overlaid within the symbol acts as anindependent channel. These independent channels differentiate thetechnique from existing modulation techniques.

With respect to the application of orbital angular momentum 804, thisembodiment introduces twisted electromagnetic waves, or light beams,having helical wave fronts that carry orbital angular momentum (OAM).Different OAM carrying waves/beams can be mutually orthogonal to eachother within the spatial domain, allowing the waves/beams to beefficiently multiplexed and demultiplexed within a communications link.OAM beams are interesting in communications due to their potentialability in special multiplexing multiple independent data carryingchannels.

With respect to the combination of quantum level overlay techniques 802and orbital angular momentum application 804, the combination is uniqueas the OAM multiplexing technique is compatible with otherelectromagnetic techniques such as wave length and polarization divisionmultiplexing. This suggests the possibility of further increasing systemperformance. The application of these techniques together in highcapacity data transmission disrupts the access part of an end to endcommunications system from twisted pair and cable to fiber optics, tofree space optics, to RF used in cellular/backhaul and satellites.

Each of these techniques can be applied independent of one another, butthe combination provides a unique opportunity to not only increasespectral efficiency, but to increase spectral efficiency withoutsacrificing distance or signal to noise ratios.

Using the Shannon Capacity Equation, a determination may be made ifspectral efficiency is increased. This can be mathematically translatedto more bandwidth. Since bandwidth has a value, one can easily convertspectral efficiency gains to financial gains for the business impact ofusing higher spectral efficiency. Also, when sophisticated forward errorcorrection (FEC) techniques are used, the net impact is higher qualitybut with the sacrifice of some bandwidth. However, if one can achievehigher spectral efficiency (or more virtual bandwidth), one cansacrifice some of the gained bandwidth for FEC and therefore higherspectral efficiency can also translate to higher quality.

Telecom operators and vendors are interested in increasing spectralefficiency. However, the issue with respect to this increase is thecost. Each technique at different layers of the protocol has a differentprice tag associated therewith. Techniques that are implemented at aphysical layer have the most impact as other techniques can besuperimposed on top of the lower layer techniques and thus increase thespectral efficiency further. The price tag for some of the techniquescan be drastic when one considers other associated costs. For example,the multiple input multiple output (MIMO) technique uses additionalantennas to create additional paths where each RF path can be treated asan independent channel and thus increase the aggregate spectralefficiency. In the MIMO scenario, the operator has other associated softcosts dealing with structural issues such as antenna installations, etc.These techniques not only have tremendous cost, but they have hugetiming issues as the structural activities take time and the achievingof higher spectral efficiency comes with significant delays which canalso be translated to financial losses.

The quantum level overlay technique 802 has an advantage that theindependent channels are created within the symbols without needing newantennas. This will have a tremendous cost and time benefit compared toother techniques. Also, the quantum layer overlay technique 802 is aphysical layer technique, which means there are other techniques athigher layers of the protocol that can all ride on top of the QLOtechniques 802 and thus increase the spectral efficiency even further.QLO technique 802 uses standard QAM modulation used in OFDM basedmultiple access technologies such as WIMAX or LTE. QLO technique 802basically enhances the QAM modulation at the transceiver by injectingnew signals to the I & Q components of the baseband and overlaying thembefore QAM modulation as will be more fully described herein below. Atthe receiver, the reverse procedure is used to separate the overlaidsignal and the net effect is a pulse shaping that allows betterlocalization of the spectrum compared to standard QAM or even the rootraised cosine. The impact of this technique is a significantly higherspectral efficiency.

Referring now more particularly to FIG. 9, there is illustrated ageneral overview of the manner for providing improved communicationbandwidth within various communication protocol interfaces 902, using acombination of multiple level overlay modulation 904 and the applicationof orbital angular momentum 906 to increase the number of communicationschannels.

The various communication protocol interfaces 902 may comprise a varietyof communication links, such as RF communication, wireline communicationsuch as cable or twisted pair connections, or optical communicationsmaking use of light wavelengths such as fiber-optic communications orfree-space optics. Various types of RF communications may include acombination of RF microwave or RF satellite communication, as well asmultiplexing between RF and free-space optics in real time.

By combining a multiple layer overlay modulation technique 904 withorbital angular momentum (OAM) technique 906, a higher throughput overvarious types of communication links 902 may be achieved. The use ofmultiple level overlay modulation alone without OAM increases thespectral efficiency of communication links 902, whether wired, optical,or wireless. However, with OAM, the increase in spectral efficiency iseven more significant.

Multiple overlay modulation techniques 904 provide a new degree offreedom beyond the conventional 2 degrees of freedom, with time T andfrequency F being independent variables in a two-dimensional notationalspace defining orthogonal axes in an information diagram. This comprisesa more general approach rather than modeling signals as fixed in eitherthe frequency or time domain. Previous modeling methods using fixed timeor fixed frequency are considered to be more limiting cases of thegeneral approach of using multiple level overlay modulation 904. Withinthe multiple level overlay modulation technique 904, signals may bedifferentiated in two-dimensional space rather than along a single axis.Thus, the information-carrying capacity of a communications channel maybe determined by a number of signals which occupy different time andfrequency coordinates and may be differentiated in a notationaltwo-dimensional space.

Within the notational two-dimensional space, minimization of the timebandwidth product, i.e., the area occupied by a signal in that space,enables denser packing, and thus, the use of more signals, with higherresulting information-carrying capacity, within an allocated channel.Given the frequency channel delta (Δf), a given signal transmittedthrough it in minimum time Δt will have an envelope described by certaintime-bandwidth minimizing signals. The time-bandwidth products for thesesignals take the form;ΔtΔf=½(2n+1)where n is an integer ranging from 0 to infinity, denoting the order ofthe signal.

These signals form an orthogonal set of infinite elements, where eachhas a finite amount of energy. They are finite in both the time domainand the frequency domain, and can be detected from a mix of othersignals and noise through correlation, for example, by match filtering.Unlike other wavelets, these orthogonal signals have similar time andfrequency forms.

The orbital angular momentum process 906 provides a twist to wave frontsof the electromagnetic fields carrying the data stream that may enablethe transmission of multiple data streams on the same frequency,wavelength, or other signal-supporting mechanism. This will increase thebandwidth over a communications link by allowing a single frequency orwavelength to support multiple eigen channels, each of the individualchannels having a different orthogonal and independent orbital angularmomentum associated therewith.

Referring now to FIG. 10, there is illustrated a further communicationimplementation technique using the above described techniques as twistedpairs or cables carry electrons (not photons). Rather than using each ofthe multiple level overlay modulation 904 and orbital angular momentumtechniques 906, only the multiple level overlay modulation 904 can beused in conjunction with a single wireline interface and, moreparticularly, a twisted pair communication link or a cable communicationlink 1002. The operation of the multiple level overlay modulation 1004,is similar to that discussed previously with respect to FIG. 9, but isused by itself without the use of orbital angular momentum techniques906, and is used with either a twisted pair communication link or cableinterface communication link 1002.

Referring now to FIG. 11, there is illustrated a general block diagramfor processing a plurality of data streams 1102 for transmission in anoptical communication system. The multiple data streams 1102 areprovided to the multi-layer overlay modulation circuitry 1104 whereinthe signals are modulated using the multi-layer overlay modulationtechnique. The modulated signals are provided to orbital angularmomentum processing circuitry 1106 which applies a twist to each of thewave fronts being transmitted on the wavelengths of the opticalcommunication channel. The twisted waves are transmitted through theoptical interface 1108 over an optical communications link such as anoptical fiber or free space optics communication system. FIG. 11 mayalso illustrate an RF mechanism wherein the interface 1108 wouldcomprise and RF interface rather than an optical interface.

Referring now more particularly to FIG. 12, there is illustrated afunctional block diagram of a system for generating the orbital angularmomentum “twist” within a communication system, such as that illustratedwith respect to FIG. 9, to provide a data stream that may be combinedwith multiple other data streams for transmission upon a same wavelengthor frequency. Multiple data streams 1202 are provided to thetransmission processing circuitry 1200. Each of the data streams 1202comprises, for example, an end to end link connection carrying a voicecall or a packet connection transmitting non-circuit switch packed dataover a data connection. The multiple data streams 1202 are processed bymodulator/demodulator circuitry 1204. The modulator/demodulatorcircuitry 1204 modulates the received data stream 1202 onto a wavelengthor frequency channel using a multiple level overlay modulationtechnique, as will be more fully described herein below. Thecommunications link may comprise an optical fiber link, free-spaceoptics link, RF microwave link, RF satellite link, wired link (withoutthe twist), etc.

The modulated data stream is provided to the orbital angular momentum(OAM) signal processing block 1206. Each of the modulated data streamsfrom the modulator/demodulator 1204 are provided a different orbitalangular momentum by the orbital angular momentum electromagnetic block1206 such that each of the modulated data streams have a unique anddifferent orbital angular momentum associated therewith. Each of themodulated signals having an associated orbital angular momentum areprovided to an optical transmitter 1208 that transmits each of themodulated data streams having a unique orbital angular momentum on asame wavelength. Each wavelength has a selected number of bandwidthslots B and may have its data transmission capability increase by afactor of the number of degrees of orbital angular momentum l that areprovided from the OAM electromagnetic block 1206. The opticaltransmitter 1208 transmitting signals at a single wavelength couldtransmit B groups of information. The optical transmitter 1208 and OAMelectromagnetic block 1206 may transmit l×B groups of informationaccording to the configuration described herein.

In a receiving mode, the optical transmitter 1208 will have a wavelengthincluding multiple signals transmitted therein having different orbitalangular momentum signals embedded therein. The optical transmitter 1208forwards these signals to the OAM signal processing block 1206, whichseparates each of the signals having different orbital angular momentumand provides the separated signals to the demodulator circuitry 1204.The demodulation process extracts the data streams 1202 from themodulated signals and provides it at the receiving end using themultiple layer overlay demodulation technique.

Referring now to FIG. 13, there is provided a more detailed functionaldescription of the OAM signal processing block 1206. Each of the inputdata streams are provided to OAM circuitry 1302. Each of the OAMcircuitry 1302 provides a different orbital angular momentum to thereceived data stream. The different orbital angular momentums areachieved by applying different currents for the generation of thesignals that are being transmitted to create a particular orbitalangular momentum associated therewith. The orbital angular momentumprovided by each of the OAM circuitries 1302 are unique to the datastream that is provided thereto. An infinite number of orbital angularmomentums may be applied to different input data streams using manydifferent currents. Each of the separately generated data streams areprovided to a signal combiner 1304, which combines the signals onto awavelength for transmission from the transmitter 1306.

Referring now to FIG. 14, there is illustrated the manner in which theOAM processing circuitry 1206 may separate a received signal intomultiple data streams. The receiver 1402 receives the combined OAMsignals on a single wavelength and provides this information to a signalseparator 1404. The signal separator 1404 separates each of the signalshaving different orbital angular momentums from the received wavelengthand provides the separated signals to OAM de-twisting circuitry 1406.The OAM de-twisting circuitry 1406 removes the associated OAM twist fromeach of the associated signals and provides the received modulated datastream for further processing. The signal separator 1404 separates eachof the received signals that have had the orbital angular momentumremoved therefrom into individual received signals. The individuallyreceived signals are provided to the receiver 1402 for demodulationusing, for example, multiple level overlay demodulation as will be morefully described herein below.

FIG. 15 illustrates in a manner in which a single wavelength orfrequency, having two quanti-spin polarizations may provide an infinitenumber of twists having various orbital angular momentums associatedtherewith. The l axis represents the various quantized orbital angularmomentum states which may be applied to a particular signal at aselected frequency or wavelength. The symbol omega (ω) represents thevarious frequencies to which the signals of differing orbital angularmomentum may be applied. The top grid 1502 represents the potentiallyavailable signals for a left handed signal polarization, while thebottom grid 1504 is for potentially available signals having righthanded polarization.

By applying different orbital angular momentum states to a signal at aparticular frequency or wavelength, a potentially infinite number ofstates may be provided at the frequency or wavelength. Thus, the stateat the frequency Δω or wavelength 1506 in both the left handedpolarization plane 1502 and the right handed polarization plane 1504 canprovide an infinite number of signals at different orbital angularmomentum states Δl. Blocks 1508 and 1510 represent a particular signalhaving an orbital angular momentum Δl at a frequency Δω or wavelength inboth the right handed polarization plane 1504 and left handedpolarization plane 1510, respectively. By changing to a differentorbital angular momentum within the same frequency Δω or wavelength1506, different signals may also be transmitted. Each angular momentumstate corresponds to a different determined current level fortransmission from the optical transmitter. By estimating the equivalentcurrent for generating a particular orbital angular momentum within theoptical domain and applying this current for transmission of thesignals, the transmission of the signal may be achieved at a desiredorbital angular momentum state.

Thus, the illustration of FIG. 15, illustrates two possible angularmomentums, the spin angular momentum, and the orbital angular momentum.The spin version is manifested within the polarizations of macroscopicelectromagnetism, and has only left and right hand polarizations due toup and down spin directions. However, the orbital angular momentumindicates an infinite number of states that are quantized. The paths aremore than two and can theoretically be infinite through the quantizedorbital angular momentum levels.

Using the orbital angular momentum state of the transmitted energysignals, physical information can be embedded within the radiationtransmitted by the signals. The Maxwell-Heaviside equations can berepresented as:

${\nabla{\cdot E}} = \frac{\rho}{ɛ_{0}}$${\nabla{\cdot E}} = {- \frac{\partial B}{\partial t}}$ ∇⋅B = 0${\nabla{\cdot B}} = {{ɛ_{0}\mu_{0}\frac{\partial E}{\partial t}} + {\mu_{0}{j\left( {t,x} \right)}}}$where ∇ is the del operator, E is the electric field intensity and B isthe magnetic flux density. Using these equations, one can derive 23symmetries/conserved quantities from Maxwell's original equations.However, there are only ten well-known conserved quantities and only afew of these are commercially used. Historically if Maxwell's equationswhere kept in their original quaternion forms, it would have been easierto see the symmetries/conserved quantities, but when they were modifiedto their present vectorial form by Heaviside, it became more difficultto see such inherent symmetries in Maxwell's equations.

Maxwell's linear theory is of U(1) symmetry with Abelian commutationrelations. They can be extended to higher symmetry group SU(2) form withnon-Abelian commutation relations that address global (non-local inspace) properties. The Wu-Yang and Harmuth interpretation of Maxwell'stheory implicates the existence of magnetic monopoles and magneticcharges. As far as the classical fields are concerned, these theoreticalconstructs are pseudo-particle, or instanton. The interpretation ofMaxwell's work actually departs in a significant ways from Maxwell'soriginal intention. In Maxwell's original formulation, Faraday'selectronic states (the Aμ field) was central making them compatible withYang-Mills theory (prior to Heaviside). The mathematical dynamicentities called solitons can be either classical or quantum, linear ornon-linear and describe EM waves. However, solitons are of SU(2)symmetry forms. In order for conventional interpreted classicalMaxwell's theory of U(1) symmetry to describe such entities, the theorymust be extended to SU(2) forms.

Besides the half dozen physical phenomena (that cannot be explained withconventional Maxwell's theory), the recently formulated Harmuth Ansatzalso address the incompleteness of Maxwell's theory. Harmuth amendedMaxwell's equations can be used to calculate EM signal velocitiesprovided that a magnetic current density and magnetic charge are addedwhich is consistent to Yang-Mills filed equations. Therefore, with thecorrect geometry and topology, the Aμ potentials always have physicalmeaning

The conserved quantities and the electromagnetic field can berepresented according to the conservation of system energy and theconservation of system linear momentum. Time symmetry, i.e. theconservation of system energy can be represented using Poynting'stheorem according to the equations:

$\begin{matrix}{H = {{\sum\limits_{i}\;{m_{i}\gamma_{i}c^{2}}} + {\frac{ɛ_{0}}{2}{\int{d^{3}{x\left( {{E}^{2} + {c^{2}{B}^{2}}} \right)}}}}}} & {{Hamiltonian}\mspace{14mu}\left( {{total}\mspace{14mu}{energy}} \right)} \\{{\frac{{dU}^{mech}}{dt} + \frac{{dU}^{em}}{dt} + {\oint_{s^{\prime}}{d^{2}x^{\prime}{\hat{n^{\prime}} \cdot S}}}} = 0} & {{conservation}\mspace{14mu}{of}\mspace{14mu}{energy}}\end{matrix}$

The space symmetry, i.e., the conservation of system linear momentumrepresenting the electromagnetic Doppler shift can be represented by theequations:

$\begin{matrix}{p = {{\sum\limits_{i}\;{m_{i}\gamma_{i}v_{i}}} + {ɛ_{0}{\int{d^{3}{x\left( {E \times B} \right)}}}}}} & {{linear}\mspace{14mu}{momentum}} \\{{\frac{{dp}^{mech}}{dt} + \frac{{dp}^{em}}{dt} + {\oint_{s^{\prime}}{d^{2}x^{\prime}{\hat{n^{\prime}} \cdot T}}}} = 0} & {{conservation}\mspace{14mu}{of}\mspace{14mu}{linear}{\mspace{11mu}\;}{momentum}}\end{matrix}$The conservation of system center of energy is represented by theequation:

$R = {{\frac{1}{H}{\sum\limits_{i}\;{\left( {x_{i} - x_{0}} \right)m_{i}\gamma_{i}c^{2}}}} + {\frac{ɛ_{0}}{2\; H}{\int{d^{3}{x\left( {x - x_{0}} \right)}\left( {{E}^{2} + {c^{2}{B}^{2}}} \right)}}}}$

Similarly, the conservation of system angular momentum, which gives riseto the azimuthal Doppler shift is represented by the equation:

$\begin{matrix}{{\frac{{dJ}^{mech}}{dt} + \frac{{dJ}^{em}}{dt} + {\oint_{s^{\prime}}{d^{2}x^{\prime}{\hat{n^{\prime}} \cdot M}}}} = 0} & {{conservation}\mspace{14mu}{of}\mspace{14mu}{angular}{\mspace{11mu}\;}{momentum}}\end{matrix}$For radiation beams in free space, the EM field angular momentum J^(em)can be separated into two parts:J ^(em)=ε₀∫_(V′) d ³ x′(E×A)+ε₀∫_(V′) d ³ x′E _(i)[(x′−x ₀)×∇]A _(i)For each singular Fourier mode in real valued representation:

$J^{em} = {{{- i}\frac{ɛ_{0}}{2\omega}{\int_{V^{\prime}}{d^{3}{x^{\prime}\left( {E^{*} \times E} \right)}}}} - {i\frac{ɛ_{0}}{2\omega}{\int_{V^{\prime}}{d^{3}x^{\prime}{E_{i}\left\lbrack {\left( {x^{\prime} - x_{0}} \right) \times \nabla} \right\rbrack}E_{i}}}}}$

The first part is the EM spin angular momentum S^(em), its classicalmanifestation is wave polarization. And the second part is the EMorbital angular momentum L^(em) its classical manifestation is wavehelicity. In general, both EM linear momentum P^(em), and EM angularmomentum J^(em)=L^(em)+S^(em) are radiated all the way to the far field.

By using Poynting theorem, the optical vorticity of the signals may bedetermined according to the optical velocity equation:

${{\frac{\partial U}{\partial t} + {\nabla{\cdot S}}} = 0},{{continuity}\mspace{14mu}{equation}}$where S is the Poynting vectorS=¼(E×H*+E*×H),and U is the energy densityU=¼(ε|E| ²+μ₀ |H| ²),with E and H comprising the electric field and the magnetic field,respectively, and ε and μ₀ being the permittivity and the permeabilityof the medium, respectively. The optical vorticity V may then bedetermined by the curl of the optical velocity according to theequation:

$V = {{\nabla{\times v_{opt}}} = {\nabla{\times \left( \frac{{E \times H^{*}} + {E^{*} \times H}}{{ɛ{E}^{2}} + {\mu_{0}{H}^{2}}} \right)}}}$

Referring now to FIGS. 16A and 16B, there is illustrated the manner inwhich a signal and its associated Poynting vector in a plane wavesituation. In the plane wave situation illustrated generally at 1602,the transmitted signal may take one of three configurations. When theelectric field vectors are in the same direction, a linear signal isprovided, as illustrated generally at 1604. Within a circularpolarization 1606, the electric field vectors rotate with the samemagnitude. Within the elliptical polarization 1608, the electric fieldvectors rotate but have differing magnitudes. The Poynting vectorremains in a constant direction for the signal configuration to FIG. 16Aand always perpendicular to the electric and magnetic fields. Referringnow to FIG. 16B, when a unique orbital angular momentum is applied to asignal as described here and above, the Poynting vector S 1610 willspiral about the direction of propagation of the signal. This spiral maybe varied in order to enable signals to be transmitted on the samefrequency as described herein.

FIGS. 17A through 17C illustrate the differences in signals havingdifferent helicity (i.e., orbital angular momentums). Each of thespiraling Poynting vectors associated with the signals 1702, 1704, and1706 provide a different shaped signal. Signal 1702 has an orbitalangular momentum of +1, signal 1704 has an orbital angular momentum of+3, and signal 1706 has an orbital angular momentum of −4. Each signalhas a distinct angular momentum and associated Poynting vector enablingthe signal to be distinguished from other signals within a samefrequency. This allows differing type of information to be transmittedon the same frequency, since these signals are separately detectable anddo not interfere with each other (Eigen channels).

FIG. 17D illustrates the propagation of Poynting vectors for variousEigen modes. Each of the rings 1720 represents a different Eigen mode ortwist representing a different orbital angular momentum within the samefrequency. Each of these rings 1720 represents a different orthogonalchannel. Each of the Eigen modes has a Poynting vector 1722 associatedtherewith.

Topological charge may be multiplexed to the frequency for either linearor circular polarization. In case of linear polarizations, topologicalcharge would be multiplexed on vertical and horizontal polarization. Incase of circular polarization, topological charge would multiplex onleft hand and right hand circular polarizations. The topological chargeis another name for the helicity index “I” or the amount of twist or OAMapplied to the signal. The helicity index may be positive or negative.In RF, different topological charges can be created and muxed togetherand de-muxed to separate the topological charges.

The topological charges l s can be created using Spiral Phase Plates(SPPs) as shown in FIG. 17E using a proper material with specific indexof refraction and ability to machine shop or phase mask, hologramscreated of new materials or a new technique to create an RF version ofSpatial Light Modulator (SLM) that does the twist of the RF waves (asopposed to optical beams) by adjusting voltages on the device resultingin twisting of the RF waves with a specific topological charge. SpiralPhase plates can transform a RF plane wave (l=0) to a twisted RF wave ofa specific helicity (i.e. l=+1).

Cross talk and multipath interference can be corrected using RFMultiple-Input-Multiple-Output (MIMO). Most of the channel impairmentscan be detected using a control or pilot channel and be corrected usingalgorithmic techniques (closed loop control system).

As described previously with respect to FIG. 17, each of the multipledata streams applied within the processing circuitry has a multiplelayer overlay modulation scheme applied thereto.

Referring now to FIG. 18, the reference number 1800 generally indicatesan embodiment of a multiple level overlay (MLO) modulation system,although it should be understood that the term MLO and the illustratedsystem 1800 are examples of embodiments. The MLO system may comprise onesuch as that disclosed in U.S. Pat. No. 8,503,546 entitled MultipleLayer Overlay Modulation which is incorporated herein by reference. Inone example, the modulation system 1800 would be implemented within themultiple level overlay modulation box 504 of FIG. 17. System 1800 takesas input an input data stream 1801 from a digital source 1802, which isseparated into three parallel, separate data streams, 1803A-1803C, oflogical 1s and 0s by input stage demultiplexer (DEMUX) 1004. Data stream1001 may represent a data file to be transferred, or an audio or videodata stream. It should be understood that a greater or lesser number ofseparated data streams may be used. In some of the embodiments, each ofthe separated data streams 1803A-1803C has a data rate of 1/N of theoriginal rate, where N is the number of parallel data streams. In theembodiment illustrated in FIG. 18, N is 3.

Each of the separated data streams 1803A-1803C is mapped to a quadratureamplitude modulation (QAM) symbol in an M-QAM constellation, forexample, 16 QAM or 64 QAM, by one of the QAM symbol mappers 1805A-C. TheQAM symbol mappers 1805A-C are coupled to respective outputs of DEMUX1804, and produced parallel in phase (I) 1806A, 1808A, and 1810A andquadrature phase (Q) 1806B, 1808B, and 1810B data streams at discretelevels. For example, in 64 QAM, each I and Q channel uses 8 discretelevels to transmit 3 bits per symbol. Each of the three I and Q pairs,1806A-1806B, 1808A-1808B, and 1810A-1810B, is used to weight the outputof the corresponding pair of function generators 1807A-1807B,1809A-1809B, and 1811A-1811B, which in some embodiments generate signalssuch as the modified Hermite polynomials described above and weightsthem based on the amplitude value of the input symbols. This provides 2N weighted or modulated signals, each carrying a portion of the dataoriginally from income data stream 1801, and is in place of modulatingeach symbol in the I and Q pairs, 1806A-1806B, 1808A-1808B, and1810A-1810B with a raised cosine filter, as would be done for a priorart QAM system. In the illustrated embodiment, three signals are used,SH0, SH1, and SH2, which correspond to modifications of H0, H1, and H2,respectively, although it should be understood that different signalsmay be used in other embodiments.

The weighted signals are not subcarriers, but rather are sublayers of amodulated carrier, and are combined, superimposed in both frequency andtime, using summers 1812 and 1816, without mutual interference in eachof the I and Q dimensions, due to the signal orthogonality. Summers 1812and 1816 act as signal combiners to produce composite signals 1813 and1817. The weighted orthogonal signals are used for both I and Qchannels, which have been processed equivalently by system 1800, and aresummed before the QAM signal is transmitted. Therefore, although neworthogonal functions are used, some embodiments additionally use QAM fortransmission. Because of the tapering of the signals in the time domain,as will be shown in FIGS. 16A through 16K, the time domain waveform ofthe weighted signals will be confined to the duration of the symbols.Further, because of the tapering of the special signals and frequencydomain, the signal will also be confined to frequency domain, minimizinginterface with signals and adjacent channels.

The composite signals 1813 and 1817 are converted to analogue signals1815 and 1819 using digital to analogue converters 1814 and 1818, andare then used to modulate a carrier signal at the frequency of localoscillator (LO) 1820, using modulator 1821. Modulator 1821 comprisesmixers 1822 and 1824 coupled to DACs 1814 and 1818, respectively. Ninetydegree phase shifter 1823 converts the signals from LO 1820 into a Qcomponent of the carrier signal. The output of mixers 1822 and 1824 aresummed in summer 1825 to produce output signals 1826.

MLO can be used with a variety of transport mediums, such as wire,optical, and wireless, and may be used in conjunction with QAM. This isbecause MLO uses spectral overlay of various signals, rather thanspectral overlap. Bandwidth utilization efficiency may be increased byan order of magnitude, through extensions of available spectralresources into multiple layers. The number of orthogonal signals isincreased from 2, cosine and sine, in the prior art, to a number limitedby the accuracy and jitter limits of generators used to produce theorthogonal polynomials. In this manner, MLO extends each of the I and Qdimensions of QAM to any multiple access techniques such as GSM, codedivision multiple access (CDMA), wide band CDMA (WCDMA), high speeddownlink packet access (HSPDA), evolution-data optimized (EV-DO),orthogonal frequency division multiplexing (OFDM), world-wideinteroperability for microwave access (WIMAX), and long term evolution(LTE) systems. MLO may be further used in conjunction with othermultiple access (MA) schemes such as frequency division duplexing (FDD),time division duplexing (TDD), frequency division multiple access(FDMA), and time division multiple access (TDMA). Overlaying individualorthogonal signals over the same frequency band allows creation of avirtual bandwidth wider than the physical bandwidth, thus adding a newdimension to signal processing. This modulation is applicable to twistedpair, cable, fiber optic, satellite, broadcast, free-space optics, andall types of wireless access. The method and system are compatible withmany current and future multiple access systems, including EV-DO, UMB,WIMAX, WCDMA (with or without), multimedia broadcast multicast service(MBMS)/multiple input multiple output (MIMO), HSPA evolution, and LTE.

Referring now to FIG. 19, an MLO demodulator 1900 is illustrated,although it should be understood that the term MLO and the illustratedsystem 1900 are examples of embodiments. The modulator 1900 takes asinput an MLO signal 1126 which may be similar to output signal 1826 fromsystem 1800. Synchronizer 1927 extracts phase information, which isinput to local oscillator 1920 to maintain coherence so that themodulator 1921 can produce base band to analogue I signal 1915 and Qsignal 1919. The modulator 1921 comprises mixers 1922 and 1924, which,coupled to OL1920 through 90 degree phase shifter 1923. I signal 1915 isinput to each of signal filters 1907A, 1909A, and 1911A, and Q signal1919 is input to each of signal filters 1907B, 1909B, and 1911B. Sincethe orthogonal functions are known, they can be separated usingcorrelation or other techniques to recover the modulated data.Information in each of the I and Q signals 1915 and 1919 can beextracted from the overlapped functions which have been summed withineach of the symbols because the functions are orthogonal in acorrelative sense.

In some embodiments, signal filters 1907A-1907B, 1909A-1909B, and1911A-1911B use locally generated replicas of the polynomials as knownsignals in match filters. The outputs of the match filters are therecovered data bits, for example, equivalence of the QAM symbols1906A-1906B, 1908A-1908B, and 1910A-1910B of system 1900. Signal filters1907A-1907B, 1909A-1909B, and 1911A-1911B produce 2 n streams of n, I,and Q signal pairs, which are input into demodulators 1928-1933.Demodulators 1928-1933 integrate the energy in their respective inputsignals to determine the value of the QAM symbol, and hence the logical1s and 0s data bit stream segment represented by the determined symbol.The outputs of the modulators 1928-1933 are then input into multiplexers(MUXs) 1905A-1905C to generate data streams 1903A-1903C. If system 1900is demodulating a signal from system 1800, data streams 1903A-1903Ccorrespond to data streams 1803A-1803C. Data streams 1903A-1903C aremultiplexed by MUX 1904 to generate data output stream 1901. In summary,MLO signals are overlayed (stacked) on top of one another on transmitterand separated on receiver.

MLO may be differentiated from CDMA or OFDM by the manner in whichorthogonality among signals is achieved. MLO signals are mutuallyorthogonal in both time and frequency domains, and can be overlaid inthe same symbol time bandwidth product. Orthogonality is attained by thecorrelation properties, for example, by least sum of squares, of theoverlaid signals. In comparison, CDMA uses orthogonal interleaving ordisplacement of signals in the time domain, whereas OFDM uses orthogonaldisplacement of signals in the frequency domain.

Bandwidth efficiency may be increased for a channel by assigning thesame channel to multiple users. This is feasible if individual userinformation is mapped to special orthogonal functions. CDMA systemsoverlap multiple user information and views time intersymbol orthogonalcode sequences to distinguish individual users, and OFDM assigns uniquesignals to each user, but which are not overlaid, are only orthogonal inthe frequency domain. Neither CDMA nor OFDM increases bandwidthefficiency. CDMA uses more bandwidth than is necessary to transmit datawhen the signal has a low signal to noise ratio (SNR). OFDM spreads dataover many subcarriers to achieve superior performance in multipathradiofrequency environments. OFDM uses a cyclic prefix OFDM to mitigatemultipath effects and a guard time to minimize intersymbol interference(ISI), and each channel is mechanistically made to behave as if thetransmitted waveform is orthogonal. (Sync function for each subcarrierin frequency domain.)

In contrast, MLO uses a set of functions which effectively form analphabet that provides more usable channels in the same bandwidth,thereby enabling high bandwidth efficiency. Some embodiments of MLO donot require the use of cyclic prefixes or guard times, and therefore,outperforms OFDM in spectral efficiency, peak to average power ratio,power consumption, and requires fewer operations per bit. In addition,embodiments of MLO are more tolerant of amplifier nonlinearities thanare CDMA and OFDM systems.

FIG. 20 illustrates an embodiment of an MLO transmitter system 2000,which receives input data stream 2001. System 2000 represents amodulator/controller 2001, which incorporates equivalent functionalityof DEMUX 1804, QAM symbol mappers 1805A-C, function generators1807A-1807B, 1809A-1809B, and 1811A-1811B, and summers 1818 and 1816 ofsystem 1800, shown in FIG. 18. However, it should be understood thatmodulator/controller 2001 may use a greater or lesser quantity ofsignals than the three illustrated in system 1800. Modulator/controller2001 may comprise an application specific integrated circuit (ASIC), afield programmable gate array (FPGA), and/or other components, whetherdiscrete circuit elements or integrated into a single integrated circuit(IC) chip.

Modulator/controller 2001 is coupled to DACs 2004 and 2007,communicating a 10 bit I signal 2002 and a 10 bit Q signal 2005,respectively. In some embodiments, I signal 2002 and Q signal 2005correspond to composite signals 1813 and 1817 of system 1800. It shouldbe understood, however, that the 10 bit capacity of I signal 2002 and Qsignal 2005 is merely representative of an embodiment. As illustrated,modulator/controller 2001 also controls DACs 2004 and 2007 using controlsignals 2003 and 2006, respectively. In some embodiments, DACs 2004 and2007 each comprise an AD5433, complementary metal oxide semiconductor(CMOS) 10 bit current output DAC. In some embodiments, multiple controlsignals are sent to each of DACs 2004 and 2007.

DACs 2004 and 2007 output analogue signals 1815 and 1819 to quadraturemodulator 1821, which is coupled to LO 1820. The output of modulator1820 is illustrated as coupled to a transmitter 2008 to transmit datawirelessly, although in some embodiments, modulator 1821 may be coupledto a fiber-optic modem, a twisted pair, a coaxial cable, or othersuitable transmission media.

FIG. 21 illustrates an embodiment of an MLO receiver system 2100 capableof receiving and demodulating signals from system 2000. System 2100receives an input signal from a receiver 2108 that may comprise inputmedium, such as RF, wired or optical. The modulator 1921 driven by LO1920 converts the input to baseband I signal 1915 and Q signal 1919. Isignal 1915 and Q signal 1919 are input to analogue to digital converter(ADC) 2109.

ADC 2109 outputs 10 bit signal 2110 to demodulator/controller 2101 andreceives a control signal 2112 from demodulator/controller 2101.Demodulator/controller 2101 may comprise an application specificintegrated circuit (ASIC), a field programmable gate array (FPGA),and/or other components, whether discrete circuit elements or integratedinto a single integrated circuit (IC) chip. Demodulator/controller 2101correlates received signals with locally generated replicas of thesignal set used, in order to perform demodulation and identify thesymbols sent. Demodulator/controller 2101 also estimates frequencyerrors and recovers the data clock, which is used to read data from theADC 2109. The clock timing is sent back to ADC 2109 using control signal2112, enabling ADC 2109 to segment the digital I and Q signals 1915 and1919. In some embodiments, multiple control signals are sent bydemodulator/controller 2101 to ADC 2109. Demodulator/controller 2101also outputs data signal 1901.

Hermite polynomials are a classical orthogonal polynomial sequence,which are the Eigenstates of a quantum harmonic oscillator. Signalsbased on Hermite polynomials possess the minimal time-bandwidth productproperty described above, and may be used for embodiments of MLOsystems. However, it should be understood that other signals may also beused, for example orthogonal polynomials such as Jacobi polynomials,Gegenbauer polynomials, Legendre polynomials, Chebyshev polynomials, andLaguerre polynomials. Q-functions are another class of functions thatcan be employed as a basis for MLO signals.

In quantum mechanics, a coherent state is a state of a quantum harmonicoscillator whose dynamics most closely resemble the oscillating behaviorof a classical harmonic oscillator system. A squeezed coherent state isany state of the quantum mechanical Hilbert space, such that theuncertainty principle is saturated. That is, the product of thecorresponding two operators takes on its minimum value. In embodimentsof an MLO system, operators correspond to time and frequency domainswherein the time-bandwidth product of the signals is minimized. Thesqueezing property of the signals allows scaling in time and frequencydomain simultaneously, without losing mutual orthogonality among thesignals in each layer. This property enables flexible implementations ofMLO systems in various communications systems.

Because signals with different orders are mutually orthogonal, they canbe overlaid to increase the spectral efficiency of a communicationchannel. For example, when n=0, the optimal baseband signal will have atime-bandwidth product of ½, which is the Nyquist Inter-SymbolInterference (ISI) criteria for avoiding ISI. However, signals withtime-bandwidth products of 3/2, 5/2, 7/2, and higher, can be overlaid toincrease spectral efficiency.

An embodiment of an MLO system uses functions based on modified Hermitepolynomials, 4 n, and are defined by:

${\psi_{n}\left( {t,\xi} \right)} = {\frac{\left( {\tanh\;\xi} \right)^{n/2}}{2^{n/2}\left( {{n!}\cosh\;\xi} \right)^{1/2}}e^{\frac{1}{2}{t^{2}{\lbrack{1 - {\tanh\;\xi}}\rbrack}}}{H_{n}\left( \frac{t}{\sqrt{2\cosh\;{\xi sinh}\;\xi}} \right)}}$where t is time, and ξ is a bandwidth utilization parameter. Plots ofΨ_(n) for n ranging from 0 to 9, along with their Fourier transforms(amplitude squared), are shown in FIGS. 5A-5K. The orthogonality ofdifferent orders of the functions may be verified by integrating:∫∫ψ_(n)(t,ξ)ψ_(m)(t,ξ)dtdξThe Hermite polynomial is defined by the contour integral:

${{H_{n}(z)} = {\frac{n!}{2\;\pi\; i}{\oint{e^{{- t^{2}} + {2{t2}}}t^{{- n} - 1}{dt}}}}},$where the contour encloses the origin and is traversed in acounterclockwise direction. Hermite polynomials are described inMathematical Methods for Physicists, by George Arfken, for example onpage 416, the disclosure of which is incorporated by reference.

FIGS. 22A-22K illustrate representative MLO signals and their respectivespectral power densities based on the modified Hermite polynomials Ψ_(n)for n ranging from 0 to 9. FIG. 22A shows plots 2201 and 2204. Plot 2201comprises a curve 2227 representing Ψ₀ plotted against a time axis 2202and an amplitude axis 2203. As can be seen in plot 2201, curve 2227approximates a Gaussian curve. Plot 2204 comprises a curve 2237representing the power spectrum of Ψ₀ plotted against a frequency axis2205 and a power axis 2206. As can be seen in plot 2204, curve 2237 alsoapproximates a Gaussian curve. Frequency domain curve 2207 is generatedusing a Fourier transform of time domain curve 2227. The units of timeand frequency on axis 2202 and 2205 are normalized for basebandanalysis, although it should be understood that since the time andfrequency units are related by the Fourier transform, a desired time orfrequency span in one domain dictates the units of the correspondingcurve in the other domain. For example, various embodiments of MLOsystems may communicate using symbol rates in the megahertz (MHz) orgigahertz (GHz) ranges and the non-0 duration of a symbol represented bycurve 2227, i.e., the time period at which curve 2227 is above 0 wouldbe compressed to the appropriate length calculated using the inverse ofthe desired symbol rate. For an available bandwidth in the megahertzrange, the non-0 duration of a time domain signal will be in themicrosecond range.

FIGS. 22B-22J show plots 2207-2224, with time domain curves 2228-2236representing Ψ₁ through Ψ₉, respectively, and their correspondingfrequency domain curves 2238-2246. As can be seen in FIGS. 22A-22J, thenumber of peaks in the time domain plots, whether positive or negative,corresponds to the number of peaks in the corresponding frequency domainplot. For example, in plot 2223 of FIG. 22J, time domain curve 2236 hasfive positive and five negative peaks. In corresponding plot 2224therefore, frequency domain curve 2246 has ten peaks.

FIG. 22K shows overlay plots 2225 and 2226, which overlay curves2227-2236 and 2237-2246, respectively. As indicated in plot 2225, thevarious time domain curves have different durations. However, in someembodiments, the non-zero durations of the time domain curves are ofsimilar lengths. For an MLO system, the number of signals usedrepresents the number of overlays and the improvement in spectralefficiency. It should be understood that, while ten signals aredisclosed in FIGS. 22A-22K, a greater or lesser quantity of signals maybe used, and that further, a different set of signals, rather than theΨ_(n) signals plotted, may be used.

MLO signals used in a modulation layer have minimum time-bandwidthproducts, which enable improvements in spectral efficiency, and arequadratically integrable. This is accomplished by overlaying multipledemultiplexed parallel data streams, transmitting them simultaneouslywithin the same bandwidth. The key to successful separation of theoverlaid data streams at the receiver is that the signals used withineach symbols period are mutually orthogonal. MLO overlays orthogonalsignals within a single symbol period. This orthogonality prevents ISIand inter-carrier interference (ICI).

Because MLO works in the baseband layer of signal processing, and someembodiments use QAM architecture, conventional wireless techniques foroptimizing air interface, or wireless segments, to other layers of theprotocol stack will also work with MLO. Techniques such as channeldiversity, equalization, error correction coding, spread spectrum,interleaving and space-time encoding are applicable to MLO. For example,time diversity using a multipath-mitigating rake receiver can also beused with MLO. MLO provides an alternative for higher order QAM, whenchannel conditions are only suitable for low order QAM, such as infading channels. MLO can also be used with CDMA to extend the number oforthogonal channels by overcoming the Walsh code limitation of CDMA. MLOcan also be applied to each tone in an OFDM signal to increase thespectral efficiency of the OFDM systems.

Embodiments of MLO systems amplitude modulate a symbol envelope tocreate sub-envelopes, rather than sub-carriers. For data encoding, eachsub-envelope is independently modulated according to N-QAM, resulting ineach sub-envelope independently carrying information, unlike OFDM.Rather than spreading information over many sub-carriers, as is done inOFDM, for MLO, each sub-envelope of the carrier carries separateinformation. This information can be recovered due to the orthogonalityof the sub-envelopes defined with respect to the sum of squares overtheir duration and/or spectrum. Pulse train synchronization or temporalcode synchronization, as needed for CDMA, is not an issue, because MLOis transparent beyond the symbol level. MLO addresses modification ofthe symbol, but since CDMA and TDMA are spreading techniques of multiplesymbol sequences over time. MLO can be used along with CDMA and TDMA.

FIG. 23 illustrates a comparison of MLO signal widths in the time andfrequency domains. Time domain envelope representations 2301-2303 ofsignals SH0-SH3 are illustrated as all having a duration T_(S). SH0-SH3may represent PSI₀-PSI₂, or may be other signals. The correspondingfrequency domain envelope representations are 2305-2307, respectively.SH0 has a bandwidth BW, SH1 has a bandwidth three times BW, and SH2 hasa bandwidth of 5 BW, which is five times as great as that of SH0. Thebandwidth used by an MLO system will be determined, at least in part, bythe widest bandwidth of any of the signals used. If each layer uses onlya single signal type within identical time windows, the spectrum willnot be fully utilized, because the lower order signals will use less ofthe available bandwidth than is used by the higher order signals.

FIG. 24 illustrates a spectral alignment of MLO signals that accountsfor the differing bandwidths of the signals, and makes spectral usagemore uniform, using SH0-SH3. Blocks 2401-2404 are frequency domainblocks of an OFDM signal with multiple subcarriers. Block 2403 isexpanded to show further detail. Block 2403 comprises a first layer 2403x comprised of multiple SH0 envelopes 2403 a-2403 o. A second layer 2403y of SH1 envelopes 2403 p-2403 t has one third the number of envelopesas the first layer. In the illustrated example, first layer 2403 x has15 SH0 envelopes, and second layer 2403 y has five SH1 envelopes. Thisis because, since the SH1 bandwidth envelope is three times as wide asthat of SH0, 15 SH0 envelopes occupy the same spectral width as five SH1envelopes. The third layer 2403 z of block 2403 comprises three SH2envelopes 2403 u-2403 w, because the SH2 envelope is five times thewidth of the SH0 envelope.

The total required bandwidth for such an implementation is a multiple ofthe least common multiple of the bandwidths of the MLO signals. In theillustrated example, the least common multiple of the bandwidth requiredfor SH0, SH1, and SH2 is 15 BW, which is a block in the frequencydomain. The OFDM-MLO signal can have multiple blocks, and the spectralefficiency of this illustrated implementation is proportional to(15+5+3)/15.

FIG. 25 illustrates another spectral alignment of MLO signals, which maybe used alternatively to alignment scheme shown in FIG. 24. In theembodiment illustrated in FIG. 25, the OFDM-MLO implementation stacksthe spectrum of SH0, SH1, and SH2 in such a way that the spectrum ineach layer is utilized uniformly. Layer 2500A comprises envelopes2501A-2501D, which includes both SH0 and SH2 envelopes. Similarly, layer2500C, comprising envelopes 2503A-2503D, includes both SH0 and SH2envelopes. Layer 2500B, however, comprising envelopes 2502A-2502D,includes only SH1 envelopes. Using the ratio of envelope sizes describedabove, it can be easily seen that BW+5 BW=3 BW+3 BW. Thus, for each SH0envelope in layer 2500A, there is one SH2 envelope also in layer 2500Cand two SH1 envelopes in layer 2500B.

Three Scenarios Compared:

1) MLO with 3 Layers defined by:

${{f_{0}(t)} = {W_{0}\mspace{11mu} e^{- \frac{t^{2}}{4}}}},{W_{0} = 0.6316}$${{f_{1}(t)} = {W_{1}t\mspace{11mu} e^{- \frac{t^{2}}{4}}}},{W_{1} \approx 0.6316}$${{f_{2}(t)} = {{W_{2}\left( {t^{2} - 1} \right)}e^{- \frac{t^{2}}{4}}}},{W_{2} \approx 0.4466}$(The current FPGA implementation uses the truncation interval of [−6,6].)2) Conventional scheme using rectangular pulse3) Conventional scheme using a square-root raised cosine (SRRC) pulsewith a roll-off factor of 0.5

For MLO pulses and SRRC pulse, the truncation interval is denoted by[−t1, t1] in the following figures. For simplicity, we used the MLOpulses defined above, which can be easily scaled in time to get thedesired time interval (say micro-seconds or nano-seconds). For the SRRCpulse, we fix the truncation interval of [−3T, 3T] where T is the symbolduration for all results presented in this document.

Bandwidth Efficiency

The X-dB bounded power spectral density bandwidth is defined as thesmallest frequency interval outside which the power spectral density(PSD) is X dB below the maximum value of the PSD. The X-dB can beconsidered as the out-of-band attenuation.

The bandwidth efficiency is expressed in Symbols per second per Hertz.The bit per second per Hertz can be obtained by multiplying the symbolsper second per Hertz with the number of bits per symbol (i.e.,multiplying with log 2 M for M-ary QAM).

Truncation of MLO pulses introduces inter-layer interferences (ILI).However, the truncation interval of [−6, 6] yields negligible ILI while[−4, 4] causes slight tolerable ILI.

The bandwidth efficiency of MLO may be enhanced by allowing inter-symbolinterference (ISI). To realize this enhancement, designing transmitterside parameters as well as developing receiver side detection algorithmsand error performance evaluation can be performed.

Referring now to FIG. 26, there is illustrated the power spectraldensity of each layer SH0-SH2 within MLO and also for the combined threelayer MLO. 2602 illustrates the power spectral density of the SH0 layer;2604 illustrates the power spectral density of the SH1 layer; 2606illustrates the power spectral density of the SH2 layer, and 2608illustrates the combined power spectral density of each layer.

Referring now to FIG. 27, there is illustrated the power spectraldensity of each layer as well as the power spectral density of thecombined three layer in a log scale. 2702 represents the SH0 layer. 2704represents the SH1 layer. 2706 represents the SH2 layer. 2708 representsthe combined layers.

Referring now to FIG. 28, there is a bandwidth efficiency comparisonversus out of band attenuation (X-dB) where quantum level overlay pulsetruncation interval is [−6,6] and the symbol rate is 1/6. Referring alsoto FIG. 29, there is illustrated the bandwidth efficiency comparisonversus out of band attenuation (X-dB) where quantum level overlay pulsetruncation interval is [−6,6] and the symbol rate is 1/4.

The QLO signals are generated from the Physicist's special Hermitefunctions:

${{f_{n}\left( {t,\alpha} \right)} = {\sqrt{\frac{\alpha}{\sqrt{\pi}{n!}2^{n}}}{H_{n}\left( {\alpha\mspace{11mu} t} \right)}\mspace{11mu} e^{- \frac{\alpha^{2}t^{2}}{2}}}},{\alpha > 0}$Note that the initial hardware implementation is using

$\alpha = \frac{1}{\sqrt{2}}$and for consistency with his part,

$\alpha = \frac{1}{\sqrt{2}}$is used in all figures related to the spectral efficiency.

Let the low-pass-equivalent power spectral density (PSD) of the combinedQLO signals be X(f) and its bandwidth be B. Here the bandwidth isdefined by one of the following criteria.

ACLR1 (First Adjacent Channel Leakage Ratio) in dBc equals:

${{ACLR}\; 1} = \frac{\int_{B/2}^{3{B/2}}{{X(f)}{df}}}{\int_{- \infty}^{\infty}{{X(f)}{df}}}$ACLR2 (Second Adjacent Channel Leakage Ratio) in dBc equals:

${{ACLR}\; 2} = \frac{\int_{3{B/2}}^{5{B/2}}{{X(f)}{df}}}{\int_{- \infty}^{\infty}{{X(f)}{df}}}$Out-of-Band Power to Total Power Ratio is:

$\frac{2{\int_{B/2}^{\infty}{{X(f)}{df}}}}{\int_{- \infty}^{\infty}{{X(f)}{df}}}$The Band-Edge PSD in dBc/100 kHz equals:

$\frac{\int_{B/2}^{\frac{B}{2} + 10^{5}}{{X(f)}{df}}}{\int_{- \infty}^{\infty}{{X(f)}{df}}}$

Referring now to FIG. 30 there is illustrated a performance comparisonusing ACLR1 and ACLR2 for both a square root raised cosine scheme and amultiple layer overlay scheme. Line 3002 illustrates the performance ofa square root raised cosine 3002 using ACLR1 versus an MLO 3004 usingACLR1. Additionally, a comparison between a square root raised cosine3006 using ACLR2 versus MLO 3008 using ACLR2 is illustrated. Table Aillustrates the performance comparison using ACLR.

TABLE A Criteria: ACLR1 ≤ −30 dBc per bandwidth Spectral EfficiencyACLR2 ≤ −43 dBc per bandwidth (Symbol/sec/Hz) Gain SRRC [−8T, 8T] β =0.22 0.8765 1.0 N Symbol Duration Layers (Tmol) QLO N = 3 Tmol = 4 1.1331.2926 [−8, 8] N = 4 Tmol = 5 1.094 1.2481 Tmol = 4 1.367 1.5596 N = 10Tmol = 8 1.185 1.3520 Tmol = 7 1.355 1.5459 Tmol = 6 1.580 1.8026 Tmol =5 1.896 2.1631 Tmol = 4 2.371 2.7051

Referring now to FIG. 31, there is illustrated a performance comparisonbetween a square root raised cosine 3102 and a MLO 3104 usingout-of-band power. Referring now also to Table B, there is illustrated amore detailed comparison of the performance using out-of-band power.

TABLE B Table 3: Performance Comparison Using Out-of-Band PowerCriterion: Out-of-band Power/ Spectral Efficiency Total Power ≤ −30 dB(Symbol/sec/Hz) Gain SRRC [−8T, 8T] β = 0.22 0.861 1.0 N Symbol DurationLayers (Tmol) QLO N = 3 Tmol = 4 1.080 1.2544 [−8, 8] N = 4 Tmol = 51.049 1.2184 Tmol = 4 1.311 1.5226 N = 10 Tmol = 8 1.152 1.3380 Tmol = 71.317 1.5296 Tmol = 6 1.536 1.7840 Tmol = 5 1.844 2.1417 Tmol = 4 2.3052.6771

Referring now to FIG. 32, there is further provided a performancecomparison between a square root raised cosine 3202 and a MLO 3204 usingband-edge PSD. A more detailed illustration of the performancecomparison is provided in Table C.

TABLE C Table 4: Performance Comparison Using Band-Edge PSD Criterion:Spectral Efficiency Band-Edge PSD = −50 dBc/100 kHz (Symbol/sec/Hz) GainSRRC [−8T, 8T] β = 0.22 0.810 1.0 N Symbol Duration Layers (Tmol) QLO N= 3 Tmol = 4 0.925 1.1420 [−8, 8] N = 4 Tmol = 5 0.912 1.1259 Tmol = 41.14 1.4074 N = 10 Tmol = 8 1.049 1.2951 Tmol = 7 1.198 1.4790 Tmol = 61.398 1.7259 Tmol = 5 1.678 2.0716 Tmol = 4 2.097 2.5889

Referring now to FIGS. 33 and 34, there are more particularlyillustrated the transmit subsystem (FIG. 33) and the receiver subsystem(FIG. 34). The transceiver is realized using basic building blocksavailable as Commercially Off The Shelf products. Modulation,demodulation and Special Hermite correlation and de-correlation areimplemented on a FPGA board. The FPGA board 3402 at the receiver 3400estimated the frequency error and recovers the data clock (as well asdata), which is used to read data from the analog-to-digital (ADC) board3406. The FGBA board 3400 also segments the digital I and Q channels.

On the transmitter side 3300, the FPGA board 3302 realizes the specialhermite correlated QAM signal as well as the necessary control signalsto control the digital-to-analog (DAC) boards 3304 to produce analog I&Qbaseband channels for the subsequent up conversion within the directconversion quad modulator 3306. The direct conversion quad modulator3306 receives an oscillator signal from oscillator 3308.

The ADC 3406 receives the I&Q signals from the quad demodulator 3408that receives an oscillator signal from 3410.

Neither power amplifier in the transmitter nor an LNA in the receiver isused since the communication will take place over a short distance. Thefrequency band of 2.4-2.5 GHz (ISM band) is selected, but any frequencyband of interest may be utilized.

MIMO uses diversity to achieve some incremental spectral efficiency.Each of the signals from the antennas acts as an independent orthogonalchannel. With QLO, the gain in spectral efficiency comes from within thesymbol and each QLO signal acts as independent channels as they are allorthogonal to one another in any permutation. However, since QLO isimplemented at the bottom of the protocol stack (physical layer), anytechnologies at higher levels of the protocol (i.e. Transport) will workwith QLO. Therefore one can use all the conventional techniques withQLO. This includes RAKE receivers and equalizers to combat fading,cyclical prefix insertion to combat time dispersion and all othertechniques using beam forming and MIMO to increase spectral efficiencyeven further.

When considering spectral efficiency of a practical wirelesscommunication system, due to possibly different practical bandwidthdefinitions (and also not strictly bandlimited nature of actual transmitsignal), the following approach would be more appropriate.

Referring now to FIG. 35, consider the equivalent discrete time system,and obtain the Shannon capacity for that system (will be denoted by Cd).Regarding the discrete time system, for example, for conventional QAMsystems in AWGN, the system will be:y[n]=ax[n]+w[n]where a is a scalar representing channel gain and amplitude scaling,x[n] is the input signal (QAM symbol) with unit average energy (scalingis embedded in a), y[n] is the demodulator (matched filter) outputsymbol, and index n is the discrete time index.

The corresponding Shannon capacity is:C _(d)=log₂(1+|a| ²/σ²)where σ2 is the noise variance (in complex dimension) and |a|2/σ2 is theSNR of the discrete time system.

Second, compute the bandwidth W based on the adopted bandwidthdefinition (e.g., bandwidth defined by −40 dBc out of band power). Ifthe symbol duration corresponding to a sample in discrete time (or thetime required to transmit C_(d) bits) is T, then the spectral efficiencycan be obtained as:C/W=C _(d)/(TW) bps/HzIn discrete time system in AWGN channels, using Turbo or similar codeswill give performance quite close to Shannon limit C_(d). Thisperformance in discrete time domain will be the same regardless of thepulse shape used. For example, using either SRRC (square root raisedcosine) pulse or a rectangle pulse gives the same C_(d) (or C_(d)/T).However, when we consider continuous time practical systems, thebandwidths of SRRC and the rectangle pulse will be different. For atypical practical bandwidth definition, the bandwidth for a SRRC pulsewill be smaller than that for the rectangle pulse and hence SRRC willgive better spectral efficiency. In other words, in discrete time systemin AWGN channels, there is little room for improvement. However, incontinuous time practical systems, there can be significant room forimprovement in spectral efficiency.

Referring now to FIG. 36, there is illustrated a PSD plot (BLANK) ofMLO, modified MLO (MMLO) and square root raised cosine (SRRC). From theillustration in FIG. 36, demonstrates the better localization propertyof MLO. An advantage of MLO is the bandwidth. FIG. 36 also illustratesthe interferences to adjacent channels will be much smaller for MLO.This will provide additional advantages in managing, allocating orpackaging spectral resources of several channels and systems, andfurther improvement in overall spectral efficiency. If the bandwidth isdefined by the −40 dBc out of band power, the within-bandwidth PSDs ofMLO and SRRC are illustrated in FIG. 37. The ratio of the bandwidths isabout 1.536. Thus, there is significant room for improvement in spectralefficiency.

Modified MLO systems are based on block-processing wherein each blockcontains N MLO symbols and each MLO symbol has L layers. MMLO can beconverted into parallel (virtual) orthogonal channels with differentchannel SNRs as illustrated in FIG. 38. The outputs provide equivalentdiscrete time parallel orthogonal channels of MMLO.

Note that the intersymbol interference caused pulse overlapping of MLOhas been addressed by the parallel orthogonal channel conversion. As anexample, the power gain of a parallel orthogonal virtual channel of MMLOwith three layers and 40 symbols per block is illustrated in FIG. 39.FIG. 39 illustrates the channel power gain of the parallel orthogonalchannels of MMLO with three layers and T_(sim)=3. By applying a waterfilling solution, an optimal power distribution across the orthogonalchannels for a fixed transmit power may be obtained. The transmit poweron the k^(th) orthogonal channel is denoted by P_(k). Then the discretetime capacity of the MMLO can be given by:

$C_{d} = {\sum\limits_{k = 1}^{k}{{\log_{2}\left( {1 + \frac{P_{k}{a_{k}}^{2}}{\sigma_{k}^{2}}} \right)}\mspace{14mu}{bits}\mspace{14mu}{per}\mspace{14mu}{block}}}$Note that K depends on the number of MLO layers, the number of MLOsymbols per block, and MLO symbol duration.For MLO pulse duration defined by [−t₁, t₁], and symbol durationT_(mlo), the MMLO block length is:T _(block)=(N−1)T _(mlo)+2t ₁Suppose the bandwidth of MMLO signal based on the adopted bandwidthdefinition (ACLR, OBP, or other) is W_(mmlo), then the practicalspectral efficiency of MMLO is given by:

$\frac{C_{d}}{W_{mmlo}\mspace{11mu} T_{block}} = {\frac{1}{W_{mmlo}\left\{ {{\left( {N - 1} \right)T_{mlo}} + {2\mspace{11mu} t_{1}}} \right\}}{\sum\limits_{k = 1}^{K}{{\log_{2}\left( {1 + \frac{P_{k}{a_{k}}^{2}}{\sigma_{k}^{2}}} \right)}\frac{bps}{Hz}}}}$

FIGS. 40-41 show the spectral efficiency comparison of MMLO with N=40symbols per block, L=3 layers, T_(mlo)=3, t₁=8, and SRRC with duration[−8T, 8T], T=1, and the roll-off factor β=0.22, at SNR of 5 dB. Twobandwidth definitions based on ACLR1 (first adjacent channel leakagepower ratio) and OBP (out of band power) are used.

FIGS. 42-43 show the spectral efficiency comparison of MMLO with L=4layers. The spectral efficiencies and the gains of MMLO for specificbandwidth definitions are shown in the following tables.

TABLE D Spectral Efficiency (bps/Hz) Gain with based on ACLR1 ≤ 30 dBcreference per bandwidth to SRRC SRRC 1.7859 1 MMLO (3 layers, Tmlo = 3)2.7928 1.5638 MMLO (4 layers, Tmlo = 3) 3.0849 1.7274

TABLE E Gain with Spectral Efficiency (bps/Hz) reference based on OBP ≤−40 dBc to SRRC SRRC 1.7046 1 MMLO (3 layers, Tmlo = 3) 2.3030 1.3510MMLO (4 layers, Tmlo = 3) 2.6697 1.5662

Referring now to FIGS. 44 and 45, there are provided basic blockdiagrams of low-pass-equivalent MMLO transmitters (FIG. 44) andreceivers (FIG. 45). The low-pass-equivalent MMLO transmitter 4400receives a number of input signals 4402 at a block-based transmitterprocessing 4404. The transmitter processing outputs signals to theSH(L−1) blocks 4406 which produce the I&Q outputs. These signals arethen all combined together at a combining circuit 4408 for transmission.

Within the baseband receiver (FIG. 45) 4500, the received signal isseparated and applied to a series of match filters 4502. The outputs ofthe match filters are then provided to the block-based receiverprocessing block 4504 to generate the various output streams.

Consider a block of N MLO-symbols with each MLO symbol carrying Lsymbols from L layers. Then there are NL symbols in a block. Define c(m,n)=symbol transmitted by the m-th MLO layer at the n-th MLO symbol.Write all NL symbols of a block as a column vector as follows:c=[c(0,0), c(1,0), . . . , c(L−1, 0), c(0,1), c(1,1), . . . , c(L−1, 1),. . . , c(L−1, N−1)]T. Then the outputs of the receiver matched filtersfor that transmitted block in an AWGN channel, defined by the columnvector y of length NL, can be given as y=H c+n, where H is an NL×NLmatrix representing the equivalent MLO channel, and n is a correlatedGaussian noise vector.

By applying SVD to H, we have H=U D VH where D is a diagonal matrixcontaining singular values. Transmitter side processing using V and thereceiver side processing UH, provides an equivalent system with NLparallel orthogonal channels, (i.e., y=H Vc+n and UH y=Dc+UH n). Theseparallel channel gains are given by diagonal elements of D. The channelSNR of these parallel channels can be computed. Note that by thetransmit and receive block-based processing, we obtain parallelorthogonal channels and hence the ISI issue has be resolved.

Since the channel SNRs of these parallel channels are not the same, wecan apply the optimal Water filling solution to compute the transmitpower on each channel given a fixed total transmit power. Using thistransmit power and corresponding channel SNR, we can compute capacity ofthe equivalent system as given in the previous report.

Issues of Fading, Multipath, and Multi-Cell Interference

Techniques used to counteract channel fading (e.g., diversitytechniques) in conventional systems can also be applied in MMLO. Forslowly-varying multi-path dispersive channels, if the channel impulseresponse can be fed back, it can be incorporated into the equivalentsystem mentioned above, by which the channel induced ISI and theintentionally introduced MMLO ISI can be addressed jointly. For fasttime-varying channels or when channel feedback is impossible, channelequalization needs to be performed at the receiver. A block-basedfrequency-domain equalization can be applied and an oversampling wouldbe required.

If we consider the same adjacent channel power leakage for MMLO and theconventional system, then the adjacent cells' interference power wouldbe approximately the same for both systems. If interference cancellationtechniques are necessary, they can also be developed for MMLO.

Scope and System Description

This report presents the symbol error probability (or symbol error rate)performance of MLO signals in additive white Gaussian noise channel withvarious inter-symbol interference levels. As a reference, theperformance of the conventional QAM without ISI is also included. Thesame QAM size is considered for all layers of MLO and the conventionalQAM.

The MLO signals are generated from the Physicist's special Hermitefunctions:

${f_{n}\left( {t,\alpha} \right)} = \sqrt{\frac{\alpha}{\sqrt{\pi}{n!}2^{n}}{H_{n}\left( {\alpha\mspace{11mu} t} \right)}\mspace{11mu} e^{- \frac{\alpha^{2}t^{2}}{2}}}$where Hn(αt) is the n^(th) order Hermite polynomial. Note that thefunctions used in the lab setup correspond to

$\alpha = \frac{1}{\sqrt{2}}$and, for consistency,

$\alpha = \frac{1}{\sqrt{2}}$is used in this report.

MLO signals with 3, 4 or 10 layers corresponding to n=0˜2, 0˜3, or 0˜9are used and the pulse duration (the range of t) is [−8, 8] in the abovefunction.

AWGN channel with perfect synchronization is considered.

The receiver consists of matched filters and conventional detectorswithout any interference cancellation, i.e., QAM slicing at the matchedfilter outputs.

${\%\mspace{14mu}{pulse}\text{-}{overlapping}} = {\frac{T_{p} - T_{sym}}{T_{p}} \times 100\%}$where Tp is the pulse duration (16 in the considered setup) and Tsym isthe reciprocal of the symbol rate in each MLO layer. The consideredcases are listed in the following table.

TABLE F % of Pulse Overlapping T_(sym) T_(p)   0% 16 16 12.5% 14 1618.75%  13 16  25% 12 16 37.5% 10 16 43.75%  9 16  50% 8 16 56.25%  7 1662.5% 6 16  75% 4 16Derivation of the Signals Used in Modulation

To do that, it would be convenient to express signal amplitude s(t) in acomplex form close to quantum mechanical formalism. Therefore thecomplex signal can be represented as:

ψ(t) = s(t) + j σ(t)where  s(t) ≡ real  signalσ(t) = imaginary  signal  (quadrature)${\sigma(t)} = {{\frac{1}{\pi}{\int_{- \infty}^{\infty}{{s(\tau)}\frac{d\;\tau}{\tau - t}{s(t)}}}} = {{- \frac{1}{\pi}}{\int_{- \infty}^{\infty}{{\sigma(t)}\frac{d\;\tau}{\tau - t}}}}}$Where s(t) and σ(t) are Hilbert transforms of one another and since σ(t)is quadratures of s(t), they have similar spectral components. That isif they were the amplitudes of sound waves, the ear could notdistinguish one form from the other.

Let us also define the Fourier transform pairs as follows:

${\psi(t)} = {\frac{1}{\pi}{\int_{- \infty}^{\infty}{{\varphi(f)}e^{j\;\omega\; t}{df}}}}$${\varphi(f)} = {\frac{1}{\pi}{\int_{- \infty}^{\infty}{{\psi(t)}e^{{- j}\;\omega\; t}{dt}}}}$ψ^(*)(t)ψ(t) = [s(t)]² + [σ(t)]² + … ≡ signal  power

Let's also normalize all moments to M₀:

M₀ = ∫₀^(τ)s(t)dt M₀ = ∫₀^(τ)φ^(*)φ df

Then the moments are as follows:

M₀ = ∫₀^(τ)s(t)dt M₁ = ∫₀^(τ)ts(t)dt M₂ = ∫₀^(τ)t²s(t)dtM_(N − 1) = ∫₀^(τ)t^(N − 1)s(t)dt

In general, one can consider the signal s(t) be represented by apolynomial of order N, to fit closely to s(t) and use the coefficient ofthe polynomial as representation of data. This is equivalent tospecifying the polynomial in such a way that its first N “moments” M_(j)shall represent the data. That is, instead of the coefficient of thepolynomial, we can use the moments. Another method is to expand thesignal s(t) in terms of a set of N orthogonal functions φ_(k)(t),instead of powers of time. Here, we can consider the data to be thecoefficients of the orthogonal expansion. One class of such orthogonalfunctions are sine and cosine functions (like in Fourier series).

Therefore we can now represent the above moments using the orthogonalfunction ψ with the following moments:

$\overset{\_}{t} = \frac{\int{{\psi^{*}(t)}t\;{\psi(t)}{dt}}}{\int{{\psi^{*}(t)}{\psi(t)}{dt}}}$$\overset{\_}{t^{2}} = \frac{\int{{\psi^{*}(t)}t^{2}\;{\psi(t)}{dt}}}{\int{{\psi^{*}(t)}{\psi(t)}{dt}}}$$\overset{\_}{t^{n}} = \frac{\int{{\psi^{*}(t)}t^{n}\;{\psi(t)}{dt}}}{\int{{\psi^{*}(t)}{\psi(t)}{dt}}}$Similarly,

$\overset{\_}{f} = \frac{\int{{\varphi^{*}(f)}f\;{\varphi(f)}{df}}}{\int{{\varphi^{*}(f)}{\varphi(f)}{df}}}$$\overset{\_}{f^{2}} = \frac{\int{{\varphi^{*}(f)}f^{2}\;{\varphi(f)}{df}}}{\int{{\varphi^{*}(f)}{\varphi(f)}{df}}}$$\overset{\_}{f^{n}} = \frac{\int{{\varphi^{*}(f)}f^{n}\;{\varphi(f)}{df}}}{\int{{\varphi^{*}(f)}{\varphi(f)}{df}}}$If we did not use complex signal, then:f=0To represent the mean values from time to frequency domains, replace:

φ(f) → ψ(t)$\left. f\rightarrow{\frac{1}{2\pi\; j}\frac{d}{dt}} \right.$These are equivalent to somewhat mysterious rule in quantum mechanicswhere classical momentum becomes an operator:

$\left. P_{x}\rightarrow{\frac{h}{2\pi\; j}\frac{\partial}{\partial x}} \right.$Therefore using the above substitutions, we have:

$\overset{\_}{f} = {\frac{\int{{\varphi^{*}(f)}f\;{\varphi(f)}{df}}}{\int{{\varphi^{*}(f)}{\varphi(f)}{df}}} = {\frac{\int{{\psi^{*}(t)}\left( \frac{1}{2\pi\; j} \right)\frac{d\;{\psi(t)}}{dt}{dt}}}{\int{{\psi^{*}(t)}{\psi(t)}{dt}}} = {\left( \frac{1}{2\pi\; j} \right)\frac{\int{\psi^{*}\frac{d\;\psi}{dt}{dt}}}{\int{\psi^{*}\psi\;{dt}}}}}}$And:

$\overset{\_}{f^{2}} = {\frac{\int{{\varphi^{*}(f)}f^{2}\;{\varphi(f)}{df}}}{\int{{\varphi^{*}(f)}{\varphi(f)}{df}}} = {\frac{\int{{\psi^{*}\left( \frac{1}{2\pi\; j} \right)}^{2}\frac{d^{2}}{{dt}^{2}}{dt}}}{\int{\psi^{*}\psi\;{dt}}} = {{- \left( \frac{1}{2\pi\; j} \right)^{2}}\frac{\int{\psi^{*}\frac{{d\;}^{2}}{{dt}^{2}}{dt}}}{\int{\psi^{*}\psi\;{dt}}}}}}$$\mspace{20mu}{\overset{\_}{t^{2}} = \frac{\int{\psi^{*}t^{2}\psi\;{dt}}}{\int{\psi^{*}\psi\;{dt}}}}$We can now define an effective duration and effective bandwidth as:

${\Delta\; t} = {\sqrt{2\pi\overset{\_}{\;\left( {t - \overset{\_}{t}} \right)^{2}}} = {2{\pi \cdot {rms}}\mspace{14mu}{in}\mspace{14mu}{time}}}$${\Delta\; f} = {\sqrt{2\pi\overset{\_}{\;\left( {f - \overset{\_}{f}} \right)^{2}}} = {2{\pi \cdot {rms}}\mspace{14mu}{in}\mspace{14mu}{frequency}}}$But we know that:(t−t)² = t ² −( t )²(f−f)² = f ² −( f )²We can simplify if we make the following substitutions:τ=t−tΨ(τ)=ψ(t)e ^(−jωτ)ω₀=ω=2π f=2πf ₀We also know that:(Δt)²(Δf)²=(ΔtΔf)²And therefore:

$\left( {\Delta\; t\;\Delta\; f} \right)^{2} = {{\frac{1}{4}\left\lbrack {4\frac{\int{{\Psi^{*}(\tau)}\tau^{2}{\Psi(\tau)}d\;\tau{\int{\frac{d\;\Psi^{*}}{d\;\tau}\frac{d\;\Psi}{d\;\tau}d\;\tau}}}}{\left( {\int{{\Psi^{*}(\tau)}\;{\psi(\tau)}d\;\tau}} \right)^{2}}} \right\rbrack} \geq \left( \frac{1}{4} \right)}$$\left( {\Delta\; t\;\Delta\; f} \right) \geq \left( \frac{1}{2} \right)$Now instead of

$\left( {\Delta\; t\;\Delta\; f} \right) \geq \left( \frac{1}{2} \right)$we are interested to force the equality

$\left( {\Delta\; t\;\Delta\; f} \right) = \left( \frac{1}{2} \right)$and see what signals satisfy the equality. Given the fixed bandwidth Δf,the most efficient transmission is one that minimizes the time-bandwidthproduct

$\left( {\Delta\; t\;\Delta\; f} \right) = \left( \frac{1}{2} \right)$For a given bandwidth Δf, the signal that minimizes the transmission inminimum time will be a Gaussian envelope. However, we are often givennot the effective bandwidth, but always the total bandwidth f₂−f₁. Now,what is the signal shape which can be transmitted through this channelin the shortest effective time and what is the effective duration?

$\left. {{\Delta\; t}==\frac{\frac{1}{\left( {2\pi} \right)^{2}}{\int_{f_{1}}^{f_{2}}{\frac{d\;\varphi^{*}}{df}\frac{d\;\varphi}{df}}}}{\int_{f_{1}}^{f_{2}}{\varphi^{*}\varphi\;{df}}}}\rightarrow\min \right.$Where φ(f) is zero outside the range f₂−f₁.

To do the minimization, we would use the calculus of variations(Lagrange's Multiplier technique). Note that the denominator is constantand therefore we only need to minimize the numerator as:

${\left. {\Delta\; t}\rightarrow\left. \min\rightarrow{\delta{\int_{f_{1}}^{f_{2}}{\left( {{\frac{d\;\varphi^{*}}{df}\frac{d\;\varphi}{df}} + {\Lambda\;\varphi^{*}\varphi}} \right){df}}}} \right. \right. = 0}$  First  Trem                               ${\delta{\int_{f_{1}}^{f_{2}}{\frac{d\;\varphi^{*}}{df}\frac{d\;\varphi}{df}{df}}}} = {{\int{\left( {{\frac{d\;\varphi^{*}}{df}\delta\frac{d\;\varphi}{df}} + {\frac{d\;\varphi}{df}\delta\frac{d\;\varphi^{*}}{df}}} \right){df}}} = {{\int{\left( {{\frac{d\;\varphi^{*}}{df}\frac{d\;{\delta\varphi}}{df}} + {\frac{d\;\varphi}{df}\frac{d\;{\delta\varphi}^{*}}{df}}} \right){df}}} = {{\left\lbrack {{\frac{d\;\varphi^{*}}{df}{\delta\varphi}} + {\frac{d\;\varphi}{df}{\delta\varphi}^{*}}} \right\rbrack_{f_{1}}^{f_{2}\;} - {\int{\left( {{\frac{d^{2}\;\varphi^{*}}{{df}^{\mspace{11mu} 2}}{\delta\varphi}} + {\frac{{d\;}^{2}\varphi}{{df}^{\mspace{11mu} 2}}{\delta\varphi}^{*}}} \right){df}}}} = {\int{\left( {{\frac{d^{2}\;\varphi^{*}}{{df}^{\mspace{11mu} 2}}{\delta\varphi}} + {\frac{{d\;}^{2}\varphi}{{df}^{\mspace{11mu} 2}}{\delta\varphi}^{*}}} \right){df}}}}}}$Second  Trem                            δ∫_(f₁)^(f₂)(Λ φ^(*)φ)df = Λ∫_(f₁)^(f₂)(φ^(*)δφ + φδφ^(*))df           ${{{Both}\mspace{14mu}{Trems}}\mspace{500mu} = {{\int{\left\lbrack {{\left( {\frac{d^{2}\;\varphi^{*}}{{df}^{\mspace{11mu} 2}} + {\Lambda\varphi}^{*}} \right){\delta\varphi}} + {\left( {\frac{{d\;}^{2}\varphi}{{df}^{\mspace{11mu} 2}} + {\Lambda\varphi}} \right){\delta\varphi}^{*}}} \right\rbrack d\; f}} = 0}}$This is only possible if and only if:

$\left( {\frac{{d\;}^{2}\varphi}{{df}^{\mspace{14mu} 2}} + {\Lambda\varphi}} \right) = 0$The solution to this is of the form

${\varphi(f)} = {\sin\; k\;{\pi\left( \frac{f - f_{1}}{f_{2} - f_{1}} \right)}}$Now if we require that the wave vanishes at infinity, but still satisfythe minimum time-bandwidth product:

$\left( {\Delta\; t\;\Delta\; f} \right) = \left( \frac{1}{2} \right)$Then we have the wave equation of a Harmonic Oscillator:

${\frac{d^{2}{\Psi(\tau)}}{d\;\tau^{2}} + {\left( {\lambda - {\alpha^{2}\tau^{2}}} \right){\Psi(\tau)}}} = 0$which vanishes at infinity only if:

λ = α(2n + 1)$\psi_{n} = {{e^{{- \frac{1}{2}}\omega^{2}\tau^{2}}\frac{d^{n}}{d\;\tau^{n}}e^{{- \alpha^{2}}\tau^{2}}}\mspace{11mu} \propto {H_{n}(\tau)}}$Where H_(n)(τ) is the Hermit functions and:(ΔtΔf)=½(2n+1)So Hermit functions H_(n)(τ) occupy information blocks of 1/2, 3/2, 5/2,. . . with 1/2 as the minimum information quanta.Squeezed States

Here we would derive the complete Eigen functions in the mostgeneralized form using quantum mechanical approach of Dirac algebra. Westart by defining the following operators:

$b = {\sqrt{\frac{m\;\omega^{\prime}}{2\hslash}}\left( {x + \frac{ip}{m\;\omega^{\prime}}} \right)}$$b^{+} = {{\sqrt{\frac{m\;\omega^{\prime}}{2\hslash}}{\left( {x - \frac{ip}{m\;\omega^{\prime}}} \right)\left\lbrack {b,b^{+}} \right\rbrack}} = 1}$a = λ b − μ b⁺ a⁺ = λ b⁺ − μ bNow we are ready to define Δx and Δp as:

$\left( {\Delta\; x} \right)^{2} = {{\frac{\hslash}{2m\;\omega}\left( \frac{\omega}{\omega^{\prime}} \right)} = {\frac{\hslash}{2m\;\omega}\left( {\lambda - \mu} \right)^{2}}}$$\left( {\Delta\; p} \right)^{2} = {{\frac{\hslash\; m\;\omega}{2}\left( \frac{\omega^{\prime}}{\omega} \right)} = {\frac{\hslash\; m\;\omega}{2}\left( {\lambda + \mu} \right)^{2}}}$${\left( {\Delta\; x} \right)^{2}\left( {\Delta\; p} \right)^{2}} = {\frac{\hslash^{2}}{4}\left( {\lambda^{2} - \mu^{2}} \right)^{2}}$${\Delta\; x\;\Delta\; p} = {{\frac{\hslash}{2}\left( {\lambda^{2} - \mu^{2}} \right)} = \frac{\hslash}{2}}$Now let parameterize differently and instead of two variables λ and μ,we would use only one variable ξ as follows:λ=sin hξμ=cos hξλ+μ=e ^(ξ)λ−μ=−e ^(−ξ)Now the Eigen states of the squeezed case are:b|β

=β|β

(λa+μa ⁺)|β

=β|β

b=UaU ⁺U=e ^(ξ/2(a) ² ^(-a) ⁺² )U ⁺(ξ)aU(ξ)=a cos hξ−a ⁺ sin hξU ⁺(ξ)a ⁺ U(ξ)=a ⁺ cos hξ−a sin hξWe can now consider the squeezed operator:

α, ξ⟩ = U(ξ)D(α)0⟩${D(\alpha)} = {e^{\frac{- {\alpha }^{2}}{2}}e^{\alpha\; a^{+}}e^{{- \alpha^{*}}a}}$$\left. \alpha \right\rangle = {\sum\limits_{n = 0}^{\infty}{\frac{\alpha^{n}}{\sqrt{n!}}e^{\frac{- {\alpha }^{2}}{2}}\left. n \right\rangle}}$$\left. \alpha \right\rangle = {e^{\frac{- {\alpha }^{2}}{2} + {\alpha\; a^{+}}}\left. 0 \right\rangle}$For a distribution P(n) we would have:

P(n) = ⟨nβ, ξ⟩²$\left\langle {{\alpha{}\beta},\xi} \right\rangle = {\sum\limits_{n = 0}^{\infty}{\frac{\alpha^{n}}{\sqrt{n!}}e^{\frac{- {\alpha }^{2}}{2}}\left\langle {{n{}\beta},\xi} \right\rangle}}$$e^{{2{zt}} - t^{2}} = {\sum\limits_{n = 0}^{\infty}\frac{{H_{n}(z)}t^{n}}{n!}}$Therefore the final result is:

$\mspace{76mu}{\left\langle {{n{}\beta},\xi} \right\rangle = {\frac{\left( {\tanh\;\xi} \right)^{n/2}}{2^{n/2}\left( {{n!}\cosh\;\xi} \right)^{2}}e^{{{- 1}/2}{({{\beta }^{2} - {\beta^{2}\tanh\;\xi}})}}{H_{n}\left( \frac{\beta}{2\sinh\mspace{11mu}\xi\mspace{11mu}\cosh\mspace{11mu}\xi} \right)}}}$Free Space Communications

An additional configuration in which the optical angular momentumprocessing and multi-layer overlay modulation technique described hereinabove may prove useful within the optical network framework is use withfree-space optics communications. Free-space optics systems provide anumber of advantages over traditional UHF RF based systems from improvedisolation between the systems, the size and the cost of thereceivers/transmitters, lack of RF licensing laws, and by combiningspace, lighting, and communication into the same system. Referring nowto FIG. 46, there is illustrated an example of the operation of afree-space communication system. The free-space communication systemutilizes a free-space optics transmitter 4602 that transmits a lightbeam 4606 to a free-space optics receiver 4604. The major differencebetween a fiber-optic network and a free-space optic network is that theinformation beam is transmitted through free space rather than over afiber-optic cable. This causes a number of link difficulties, which willbe more fully discussed herein below. Free-space optics is a line ofsight technology that uses the invisible beams of light to provideoptical bandwidth connections that can send and receive up to 2.5 Gbpsof data, voice, and video communications between a transmitter 4602 anda receiver 4604. Free-space optics uses the same concepts asfiber-optics, except without the use of a fiber-optic cable. Free-spaceoptics systems provide the light beam 4606 within the infrared (IR)spectrum, which is at the low end of the light spectrum. Specifically,the optical signal is in the range of 300 Gigahertz to 1 Terahertz interms of wavelength.

Presently existing free-space optics systems can provide data rates ofup to 10 Gigabits per second at a distance of up to 2.5 kilometers. Inouter space, the communications range of free space opticalcommunications is currently on the order of several thousand kilometers,but has the potential to bridge interplanetary distances of millions ofkilometers, using optical telescopes as beam expanders. In January of2013, NASA used lasers to beam an image of the Mona Lisa to the LunarReconnaissance Orbiter roughly 240,000 miles away. To compensate foratmospheric interference, an error correction code algorithm, similar tothat used within compact discs, was implemented.

The distance records for optical communications involve detection andemission of laser light by space probes. A two-way distance record forcommunication was established by the Mercury Laser Altimeter instrumentaboard the MESSENGER spacecraft. This infrared diode neodymium laser,designed as a laser altimeter for a Mercury Orbiter mission, was able tocommunicate across a distance of roughly 15,000,000 miles (24,000,000kilometers) as the craft neared Earth on a fly by in May of 2005. Theprevious record had been set with a one-way detection of laser lightfrom Earth by the Galileo Probe as two ground based lasers were seenfrom 6,000,000 kilometers by the outbound probe in 1992. Researchersused a white LED based space lighting system for indoor local areanetwork communications.

Referring now to FIG. 47, there is illustrated a block diagram of afree-space optics system using orbital angular momentum and multileveloverlay modulation according to the present disclosure. The OAM twistedsignals, in addition to being transmitted over fiber, may also betransmitted using free optics. In this case, the transmission signalsare generated within transmission circuitry 4702 at each of the FSOtransceivers 4704. Free-space optics technology is based on theconnectivity between the FSO based optical wireless units, eachconsisting of an optical transceiver 4704 with a transmitter 4702 and areceiver 4706 to provide full duplex open pair and bidirectional closedpairing capability. Each optical wireless transceiver unit 4704additionally includes an optical source 4708 plus a lens or telescope4710 for transmitting light through the atmosphere to another lens 4710receiving the information. At this point, the receiving lens ortelescope 4710 connects to a high sensitivity receiver 4706 via opticalfiber 4712. The transmitting transceiver 4704 a and the receivingtransceiver 4704 b have to have line of sight to each other. Trees,buildings, animals, and atmospheric conditions all can hinder the lineof sight needed for this communications medium. Since line of sight isso critical, some systems make use of beam divergence or a diffused beamapproach, which involves a large field of view that toleratessubstantial line of sight interference without significant impact onoverall signal quality. The system may also be equipped with autotracking mechanism 4714 that maintains a tightly focused beam on thereceiving transceiver 3404 b, even when the transceivers are mounted ontall buildings or other structures that sway.

The modulated light source used with optical source 4708 is typically alaser or light emitting diode (LED) providing the transmitted opticalsignal that determines all the transmitter capabilities of the system.Only the detector sensitivity within the receiver 4706 plays an equallyimportant role in total system performance. For telecommunicationspurposes, only lasers that are capable of being modulated at 20 Megabitsper second to 2.5 Gigabits per second can meet current marketplacedemands. Additionally, how the device is modulated and how muchmodulated power is produced are both important to the selection of thedevice. Lasers in the 780-850 nm and 1520-1600 nm spectral bands meetfrequency requirements.

Commercially available FSO systems operate in the near IR wavelengthrange between 750 and 1600 nm, with one or two systems being developedto operate at the IR wavelength of 10,000 nm. The physics andtransmissions properties of optical energy as it travels through theatmosphere are similar throughout the visible and near IR wavelengthrange, but several factors that influence which wavelengths are chosenfor a particular system.

The atmosphere is considered to be highly transparent in the visible andnear IR wavelength. However, certain wavelengths or wavelength bands canexperience severe absorption. In the near IR wavelength, absorptionoccurs primarily in response to water particles (i.e., moisture) whichare an inherent part of the atmosphere, even under clear weatherconditions. There are several transmission windows that are nearlytransparent (i.e., have an attenuation of less than 0.2 dB perkilometer) within the 700-10,000 nm wavelength range. These wavelengthsare located around specific center wavelengths, with the majority offree-space optics systems designed to operate in the windows of 780-850nm and 1520-1600 nm.

Wavelengths in the 780-850 nm range are suitable for free-space opticsoperation and higher power laser sources may operate in this range. At780 nm, inexpensive CD lasers may be used, but the average lifespan ofthese lasers can be an issue. These issues may be addressed by runningthe lasers at a fraction of their maximum rated output power which willgreatly increase their lifespan. At around 850 nm, the optical source4708 may comprise an inexpensive, high performance transmitter anddetector components that are readily available and commonly used innetwork transmission equipment. Highly sensitive silicon (SI) avalanchephotodiodes (APD) detector technology and advanced vertical cavityemitting laser may be utilized within the optical source 4708.

VCSEL technology may be used for operation in the 780 to 850 nm range.Possible disadvantage of this technology include beam detection throughthe use of a night vision scope, although it is still not possible todemodulate a perceived light beam using this technique.

Wavelengths in the 1520-1600 nm range are well-suited for free-spacetransmission, and high quality transmitter and detector components arereadily available for use within the optical source block 4708. Thecombination of low attenuation and high component availability withinthis wavelength range makes the development of wavelength divisionmultiplexing (WDM) free-space optics systems feasible. However,components are generally more expensive and detectors are typically lesssensitive and have a smaller receive surface area when compared withsilicon avalanche photodiode detectors that operator at the 850 nmwavelength. These wavelengths are compatible with erbium-doped fiberamplifier technology, which is important for high power (greater than500 milliwatt) and high data rate (greater than 2.5 Gigabytes persecond) systems. Fifty to 65 times as much power can be transmitted atthe 1520-1600 nm wavelength than can be transmitted at the 780-850 nmwavelength for the same eye safety classification. Disadvantages ofthese wavelengths include the inability to detect a beam with a nightvision scope. The night vision scope is one technique that may be usedfor aligning the beam through the alignment circuitry 4714. Class 1lasers are safe under reasonably foreseeable operating conditionsincluding the use of optical instruments for intrabeam viewing. Class 1systems can be installed at any location without restriction.

Another potential optical source 4708 comprised Class 1M lasers. Class1M laser systems operate in the wavelength range from 302.5 to 4000 nm,which is safe under reasonably foreseeable conditions, but may behazardous if the user employs optical instruments within some portion ofthe beam path. As a result, Class 1M systems should only be installed inlocations where the unsafe use of optical aids can be prevented.Examples of various characteristics of both Class 1 and Class 1M lasersthat may be used for the optical source 4708 are illustrated in Table Gbelow.

TABLE G Laser Power Aperture Size Distance Power Density Classification(mW) (mm) (m) (mW/cm²)  850-nm Wavelength Class 1 0.78 7 14 2.03 50 20000.04 Class 1M 0.78 7 100 2.03 500 7 14 1299.88 50 2000 25.48 1550-nmWavelength Class 1 10 7 14 26.00 25 2000 2.04 Class 1M 10 3.5 100 103.99500 7 14 1299.88 25 2000 101.91

The 10,000 nm wavelength is relatively new to the commercial free spaceoptic arena and is being developed because of better fog transmissioncapabilities. There is presently considerable debate regarding thesecharacteristics because they are heavily dependent upon fog type andduration. Few components are available at the 10,000 nm wavelength, asit is normally not used within telecommunications equipment.Additionally, 10,000 nm energy does not penetrate glass, so it isill-suited to behind window deployment.

Within these wavelength windows, FSO systems should have the followingcharacteristics. The system should have the ability to operate at higherpower levels, which is important for longer distance FSO systemtransmissions. The system should have the ability to provide high speedmodulation, which is important for high speed FSO systems. The systemshould provide a small footprint and low power consumption, which isimportant for overall system design and maintenance. The system shouldhave the ability to operate over a wide temperature range without majorperformance degradations such that the systems may prove useful foroutdoor systems. Additionally, the mean time between failures shouldexceed 10 years. Presently existing FSO systems generally use VCSELS foroperation in the shorter IR wavelength range, and Fabry-Pérot ordistributed feedback lasers for operation in the longer IR wavelengthrange. Several other laser types are suitable for high performance FSOsystems.

A free-space optics system using orbital angular momentum processing andmulti-layer overlay modulation would provide a number of advantages. Thesystem would be very convenient. Free-space optics provides a wirelesssolution to a last-mile connection, or a connection between twobuildings. There is no necessity to dig or bury fiber cable. Free-spaceoptics also requires no RF license. The system is upgradeable and itsopen interfaces support equipment from a variety of vendors. The systemcan be deployed behind windows, eliminating the need for costly rooftopright. It is also immune to radiofrequency interference or saturation.The system is also fairly speedy. The system provides 2.5 Gigabits persecond of data throughput. This provides ample bandwidth to transferfiles between two sites. With the growth in the size of files,free-space optics provides the necessary bandwidth to transfer thesefiles efficiently.

Free-space optics also provides a secure wireless solution. The laserbeam cannot be detected with a spectral analyzer or RF meter. The beamis invisible, which makes it difficult to find. The laser beam that isused to transmit and receive the data is very narrow. This means that itis almost impossible to intercept the data being transmitted. One wouldhave to be within the line of sight between the receiver and thetransmitter in order to be able to accomplish this feat. If this occurs,this would alert the receiving site that a connection has been lost.Thus, minimal security upgrades would be required for a free-spaceoptics system.

However, there are several weaknesses with free-space optics systems.The distance of a free-space optics system is very limited. Currentlyoperating distances are approximately within 2 kilometers. Although thisis a powerful system with great throughput, the limitation of distanceis a big deterrent for full-scale implementation. Additionally, allsystems require line of sight be maintained at all times duringtransmission. Any obstacle, be it environmental or animals can hinderthe transmission. Free-space optic technology must be designed to combatchanges in the atmosphere which can affect free-space optic systemperformance capacity.

Something that may affect a free-space optics system is fog. Dense fogis a primary challenge to the operation of free-space optics systems.Rain and snow have little effect on free-space optics technology, butfog is different. Fog is a vapor composed of water droplets which areonly a few hundred microns in diameter, but can modify lightcharacteristics or completely hinder the passage of light through acombination of absorption, scattering, and reflection. The primaryanswer to counter fog when deploying free-space optic based wirelessproducts is through a network design that shortens FSO linked distancesand adds network redundancies.

Absorption is another problem. Absorption occurs when suspended watermolecules in the terrestrial atmosphere extinguish photons. This causesa decrease in the power density (attenuation) of the free space opticsbeam and directly affects the availability of the system. Absorptionoccurs more readily at some wavelengths than others. However, the use ofappropriate power based on atmospheric conditions and the use of spatialdiversity (multiple beams within an FSO based unit), helps maintain therequired level of network availability.

Solar interference is also a problem. Free-space optics systems use ahigh sensitivity receiver in combination with a larger aperture lens. Asa result, natural background light can potentially interfere withfree-space optics signal reception. This is especially the case with thehigh levels of background radiation associated with intense sunlight. Insome instances, direct sunlight may case link outages for periods ofseveral minutes when the sun is within the receiver's field of vision.However, the times when the receiver is most susceptible to the effectsof direct solar illumination can be easily predicted. When directexposure of the equipment cannot be avoided, the narrowing of receiverfield of vision and/or using narrow bandwidth light filters can improvesystem performance. Interference caused by sunlight reflecting off of aglass surface is also possible.

Scattering issues may also affect connection availability. Scattering iscaused when the wavelength collides with the scatterer. The physicalsize of the scatterer determines the type of scattering. When thescatterer is smaller than the wavelength, this is known as Rayleighscattering. When a scatterer is of comparable size to the wavelengths,this is known as Mie scattering. When the scattering is much larger thanthe wavelength, this is known as non-selective scattering. Inscattering, unlike absorption, there is no loss of energy, only adirectional redistribution of energy that may have significant reductionin beam intensity over longer distances.

Physical obstructions such as flying birds or construction cranes canalso temporarily block a single beam free space optics system, but thistends to cause only short interruptions. Transmissions are easily andautomatically resumed when the obstacle moves. Optical wireless productsuse multibeams (spatial diversity) to address temporary abstractions aswell as other atmospheric conditions, to provide for greateravailability.

The movement of buildings can upset receiver and transmitter alignment.Free-space optics based optical wireless offerings use divergent beamsto maintain connectivity. When combined with tracking mechanisms,multiple beam FSO based systems provide even greater performance andenhanced installation simplicity.

Scintillation is caused by heated air rising from the Earth or man-madedevices such as heating ducts that create temperature variations amongdifferent pockets of air. This can cause fluctuations in signalamplitude, which leads to “image dancing” at the free-space optics basedreceiver end. The effects of this scintillation are called “refractiveturbulence.” This causes primarily two effects on the optical beams.Beam wander is caused by the turbulent eddies that are no larger thanthe beam. Beam spreading is the spread of an optical beam as itpropagates through the atmosphere.

Referring now to FIGS. 48A through 48D, in order to achieve higher datacapacity within optical links, an additional degree of freedom frommultiplexing multiple data channels must be exploited. Moreover, theability to use two different orthogonal multiplexing techniques togetherhas the potential to dramatically enhance system performance andincreased bandwidth.

One multiplexing technique which may exploit the possibilities is modedivision multiplexing (MDM) using orbital angular momentum (OAM). OAMmode refers to laser beams within a free-space optical system orfiber-optic system that have a phase term of e^(ilφ) in their wavefronts, in which φ is the azimuth angle and l determines the OAM value(topological charge). In general, OAM modes have a “donut-like” ringshaped intensity distribution. Multiple spatial collocated laser beams,which carry different OAM values, are orthogonal to each other and canbe used to transmit multiple independent data channels on the samewavelength. Consequently, the system capacity and spectral efficiency interms of bits/S/Hz can be dramatically increased. Free-spacecommunications links using OAM may support 100 Tbits/capacity. Varioustechniques for implementing this as illustrated in FIGS. 48A through 48Dinclude a combination of multiple beams 4802 having multiple differentOAM values 4804 on each wavelength. Thus, beam 4802 includes OAM values,OAM1 and OAM4. Beam 4806 includes OAM value 2 and OAM value 5. Finally,beam 4808 includes OAM3 value and OAM6 value. Referring now to FIG. 48B,there is illustrated a single beam wavelength 4810 using a first groupof OAM values 4812 having both a positive OAM value 4812 and a negativeOAM value 4814. Similarly, OAM2 value may have a positive value 4816 anda negative value 4818 on the same wavelength 4810.

FIG. 48C illustrates the use of a wavelength 4820 having polarizationmultiplexing of OAM value. The wavelength 4820 can have multiple OAMvalues 4822 multiplexed thereon. The number of available channels can befurther increased by applying left or right handed polarization to theOAM values. Finally, FIG. 48D illustrates two groups of concentric rings4860, 4862 for a wavelength having multiple OAM values.

Wavelength distribution multiplexing (WDM) has been widely used toimprove the optical communication capacity within both fiber-opticsystems and free-space communication system. OAM mode multiplexing andWDM are mutually orthogonal such that they can be combined to achieve adramatic increase in system capacity. Referring now to FIG. 49, there isillustrated a scenario where each WDM channel 4902 contains manyorthogonal OAM beam 4904. Thus, using a combination of orbital angularmomentum with wave division multiplexing, a significant enhancement incommunication link to capacity may be achieved.

Current optical communication architectures have considerable routingchallenges. A routing protocol for use with free-space optic system musttake into account the line of sight requirements for opticalcommunications within a free-space optics system. Thus, a free-spaceoptics network must be modeled as a directed hierarchical random sectorgeometric graph in which sensors route their data via multi-hop paths toa base station through a cluster head. This is a new efficient routingalgorithm for local neighborhood discovery and a base station uplink anddownlink discovery algorithm. The routing protocol requires order Olog(n) storage at each node versus order O(n) used within currenttechniques and architectures.

Current routing protocols are based on link state, distance vectors,path vectors, or source routing, and they differ from the new routingtechnique in significant manners. First, current techniques assume thata fraction of the links are bidirectional. This is not true within afree-space optic network in which all links are unidirectional. Second,many current protocols are designed for ad hoc networks in which therouting protocol is designed to support multi-hop communications betweenany pair of nodes. The goal of the sensor network is to route sensorreadings to the base station. Therefore, the dominant traffic patternsare different from those in an ad hoc network. In a sensor network, nodeto base stations, base station to nodes, and local neighborhoodcommunication are mostly used.

Recent studies have considered the effect of unidirectional links andreport that as many as 5 percent to 10 percent of links and wireless adhoc networks are unidirectional due to various factors. Routingprotocols such as DSDV and AODV use a reverse path technique, implicitlyignoring such unidirectional links and are therefore not relevant inthis scenario. Other protocols such as DSR, ZRP, or ZRL have beendesigned or modified to accommodate unidirectionality by detectingunidirectional links and then providing bidirectional abstraction forsuch links. Referring now to FIG. 50, the simplest and most efficientsolution for dealing with unidirectionality is tunneling, in whichbidirectionality is emulated for a unidirectional link by usingbidirectional links on a reverse back channel to establish the tunnel.Tunneling also prevents implosion of acknowledgement packets and loopingby simply pressing link layer acknowledgements for tunneled packetsreceived on a unidirectional link. Tunneling, however, works well inmostly bidirectional networks with few unidirectional links.

Within a network using only unidirectional links such as a free-spaceoptical network, systems such as that illustrated in FIGS. 50 and 51would be more applicable. Nodes within a unidirectional network utilizea directional transmit 5002 transmitting from the node 5000 in a single,defined direction. Additionally, each node 5000 includes anomnidirectional receiver 5004 which can receive a signal coming to thenode in any direction. Also, as discussed here and above, the node 5000would also include a 0 log(n) storage 5006. Thus, each node 5000 provideonly unidirectional communications links. Thus, a series of nodes 5100as illustrated in FIG. 51 may unidirectionally communicate with anyother node 5100 and forward communication from one desk location toanother through a sequence of interconnected nodes.

Topological charge may be multiplexed to the wave length for eitherlinear or circular polarization. In the case of linear polarizations,topological charge would be multiplexed on vertical and horizontalpolarization. In case of circular polarization, topological charge wouldbe multiplexed on left hand and right hand circular polarizations.

The topological charges can be created using Spiral Phase Plates (SPPs)such as that illustrated in FIG. 17E, phase mask holograms or a SpatialLight Modulator (SLM) by adjusting the voltages on SLM which createsproperly varying index of refraction resulting in twisting of the beamwith a specific topological charge. Different topological charges can becreated and muxed together and de-muxed to separate charges.

As Spiral Phase plates can transform a plane wave (l=0) to a twistedwave of a specific helicity (i.e. l=+1), Quarter Wave Plates (QWP) cantransform a linear polarization (s=0) to circular polarization (i.e.s=+1).

Cross talk and multipath interference can be reduced usingMultiple-Input-Multiple-Output (MIMO).

Most of the channel impairments can be detected using a control or pilotchannel and be corrected using algorithmic techniques (closed loopcontrol system).

Multiplexing of the topological charge to the RF as well as free spaceoptics in real time provides redundancy and better capacity. Whenchannel impairments from atmospheric disturbances or scintillationimpact the information signals, it is possible to toggle between freespace optics to RF and back in real time. This approach still usestwisted waves on both the free space optics as well as the RF signal.Most of the channel impairments can be detected using a control or pilotchannel and be corrected using algorithmic techniques (closed loopcontrol system) or by toggling between the RF and free space optics.

In a further embodiment illustrated in FIG. 52, both RF signals and freespace optics may be implemented within a dual RF and free space opticsmechanism 5202. The dual RF and free space optics mechanism 5202 includea free space optics projection portion 5204 that transmits a light wavehaving an orbital angular momentum applied thereto with multileveloverlay modulation and a RF portion 5206 including circuitry necessaryfor transmitting information with orbital angular momentum andmultilayer overlay on an RF signal 5210. The dual RF and free spaceoptics mechanism 5202 may be multiplexed in real time between the freespace optics signal 5208 and the RF signal 5210 depending upon operatingconditions. In some situations, the free space optics signal 5208 wouldbe most appropriate for transmitting the data. In other situations, thefree space optics signal 5208 would not be available and the RF signal5210 would be most appropriate for transmitting data. The dual RF andfree space optics mechanism 5202 may multiplex in real time betweenthese two signals based upon the available operating conditions.

Multiplexing of the topological charge to the RF as well as free spaceoptics in real time provides redundancy and better capacity. Whenchannel impairments from atmospheric disturbances or scintillationimpact the information signals, it is possible to toggle between freespace optics to RF and back in real time. This approach still usestwisted waves on both the free space optics as well as the RF signal.Most of the channel impairments can be detected using a control or pilotchannel and be corrected using algorithmic techniques (closed loopcontrol system) or by toggling between the RF and free space optics.

Referring now to referring now to FIG. 53, there is illustrated a VCSEL5302. Since one VCSEL 5302 is located on the outside of a window and asecond VCSEL is located on the inside of the window, there must be somemanner for aligning the optical transmission links that are providedfrom one VCSEL to the other. One manner in which this alignment may beachieved is by having alignment holes 5304 located at multiple positionson the VCSEL 5302. In the embodiment illustrated in FIG. 53, thealignment holes 5304 are located at each corner of the VCSEL 5302. Thesealignment holes 5304 are used in the manner illustrated in FIG. 54 toalign a first VCSEL 5302 a with a second VCSEL 5302 b. Thus, by visuallyaligning each of the alignment holes 5304 located at each corner of theVCSEL 5302 a and VCSEL 5302 b, the optical transmission circuitry withinthe VCSELs may be aligned.

Rather than using the external power inputs illustrated with respect toFIG. 53, the VCSEL 5302 located on a window may be powered using othermethods as illustrated in FIG. 55, FIG. 53 illustrates a VCSEL 5302 onan interior of a window or wall 5304 and a VCSEL 5306 located on anexterior of a window or wall. Power 5308 is provided directly to theinternal VCSEL 5302 via some type of input connection. A power couplingdevice 5310 within the internal VCSEL 5302 couples with a similar powercoupling device 5312 within the external VCSEL 5306. If the VCSEL's 5302and 5304 are located on a transparent window, a photo inductor or othertype of optical power coupler may be utilized for power coupling devices5310 and 5312. If the VCSEL's 5302 and 5304 are located on oppositesides of an opaque wall, inductive coupling devices such as coil anddoctors may be used for power coupling devices 5310, 5312. In thismanner, the power coupling devices 5310 provides power to the powercoupling device 5312 to power the external VCSEL 5306.

Referring now to FIG. 56, there is illustrated an alternative embodimentwherein rather than using a VCSEL for transmission of the signal througha window or wall, a horn or conical antenna is used for the transmissionof signals through the window or wall. The signals transmitted via thehorn antennas are amplified for transmission in order to overcome thelosses caused by transmission of the signals through the window/wall.The device provides an optical or RF tunnel through the window or wallwithout requiring the drilling of any holes. The millimeter wavetransmission system 5602 includes an exterior portion 5604 located on anexterior of a window or wall 5606 and an interior portion 5608 locatedon the interior of the wall or window. The exterior portion 5604includes an antenna 5610 for transmitting and receiving signals to anexterior source. In a preferred embodiment, the antenna comprises a 28GHz antenna. However, it will be realized by one skilled in the art thatother antenna operating bandwidths may be utilized.

The transmitted and received signals are processed at a 28 GHzcirculator 5612. The circulator 5612 comprises an RF switch forswitching between three ports within the exterior portion 5604 and hasgood isolation. Within the circulator 5612 signals input at port 2 areoutput at port 3 and signals input at port 1 are output to port 2. Thus,the signals received by the antenna 5610 are provided to port 2 of thecirculator 5612 and output to port 3. The port 3 signals are provided tothe input of a power amplifier 5614. Similarly, the output of a poweramplifier 5616 is connected to input port 1 such that signals to betransmitted are provided to port 2 of the circulator 5612 fortransmission by antenna 5610.

The power amplifier 5612 boosts the signal strength for transmissionthrough the window or wall. The signals output from the power amplifier5614 are provided to a horn antenna 5618. The horn antenna 5618transmits to the RF signals provided from the power amplifier 5614through the window or wall 5606 to a receiving horn antenna 5620. Thehorn antennas may transmit/receive over a wide frequency band from 24GHz up to e-band. Within this range a particular band of operation forthe horn antennas is utilized. These bands include but are not limitedto 24 GHz band; 28 GHz A1 band; 28 GHz B1, A3 and B2 bands; 31 GHz bandand 39 GHz band. The horn antennas may also be of different sizes toprovide for example 10 db or 20 dB of gain.

The received signals are output from the horn antenna 5620 todemodulator circuit 5622 for demodulation. The demodulator 5622, inaddition to receiving the receive signal from for an antenna 5620,receives a signal output from a phase locked loop/local oscillator 5624.The phase locked loop/local oscillator 5624 is controlled responsive toa clock generation circuit 5626. The demodulated signal is provided fromthe demodulator 5622 to analog-to-digital converter 5628 to generate adigital output. The digital signal is routed via a router 5632 to theappropriate receiving party within the structure.

Signals to be transmitted are received from inside the building at therouter 5630. The router 5630 provides digital signals to a digital toanalog converter 5632 that converts the digital data signals into ananalog format. The analog signals are next modulated by a modulator5634. The modulator 5634 modulates the signals responsive to input fromthe phase locked loop/local oscillator 5624 under control of the clockgeneration circuit 5626. The modulated signals from modulator 5634 aretransmitted through the window/wall 5606 using a horn antenna 5636. Thesignals transmitted by horn antenna 5636 are received by a receivinghorn antenna 5638 located on the outside. The output of the horn antenna5638 is provided to the input of power amplifier 5616 that amplifies thesignal for transmission from the antenna 5610 after passing throughcirculator 5612. While the above discussion has been made with respectto the use of horn antennas for transmission through the window/wall,conical antennas may also be used for the transmissions through thewindow or wall.

Referring now to FIG. 57, there is illustrated the downlink lossesbetween the transmitting antenna 5610 and the receiving circuitry withinthe inside portion 5608. The signal is received at −110 dBm. Thereceiving antenna has a gain of 45 dB and a loss of 2 dB. Thus, thesignal output from the receiving antenna 5610 has a strength of −67 dBm.The circulator 5612 has a 2 dB loss, and the signal from the circulator5612 has a strength of −69 dBm. The power amplifier 5614 provides a 27dB to boost the signal to −42 dBm for transmission across thewindow/wall. The horn antenna 5618 provides a gain of 10 dBi to transmitthe signal at 32 dBm. The window/wall provides a 40 dB loss. The receivehorn antenna 5620 receives the signal at −72 dBm and provides a gain of10 dBi to output the received signal at −62 dBm to the interior circuitcomponents.

Referring now to FIG. 58, there is illustrated the uplink signalstrengths when a power amplifier is located outside the window/wall5606. The transmitted signal has a strength of 18 dBm prior to reachingthe input of the horn antenna 5636. The antenna 5636 provides a gain of10 dBi to transmit the signal at 28 dBm. The window/wall 5606 causes a40 dB total loss dropping the signal strength to −12 dB. The hornantenna 5638 provides a 10 dBi gain to the signal and outputs the signalat −2 dBm. The power amplifier 5616 provides a 26 dB gain to output thesignal at 24 dBm to the port 1 input of the circulator 5612. The powercirculator 5612 provides a further 2 dB loss to output the signal to theantenna 5610 at 22 dBm. The signal is transmitted from the antenna 5610having a gain of 45 dB and a loss of 2 dB to provide a transmittedsignal strength of 65 dBm.

Referring now to FIG. 59, there is illustrated the uplink signalstrengths when the power amplifier 5902 is located inside of thebuilding. The internal power amplifier 5902 is used when one needs morepower to be transmitted from the inside terminal. Prior to input to thepower amplifier 5902 the signal has a strength of 18 dBm within thebuilding. The power amplifier 5902 provides a 26 dB gain to transmit thesignal at 44 dBm to the input of the horn antenna 5636. The horn antenna5636 provides a 10 dBi gain and the transmitted RF signal is at 54 dBm.The transmitted signal experiences a 40 dB loss through the window/wall5604 that drops the signal strength to 14 dBm on the outside portion ofthe window/wall 5604. The receiving horn antenna 5638 provides a gain of10 dBi to increase the signal strength to 24 dBm at the output of thehorn antenna 5638 that is provided to port 1 of the circulator 5612. Thecirculator 5612 causes a 2 dB loss to drop the signal strength to 22dBm. The transmitting antenna 5610 provides a further gain of 45 dB andloss off 2 dB to provide a transmitted output signal strength of 65 dBm.

Referring now to FIG. 60, there is illustrated the gains and losses onthe downlink when no power amplifier is included. A signal having a −103dBm strength is received by the antenna 5610. The antenna 5610 providesa gain of 45 dB and a loss of 2 dB. This provides a 60 DBM signal at theoutput of the antenna 5610 that is input to port 2 of the circulator5612. The circulator 5612 provides a further 2 dB loss to the signalproviding a −62 dBm signal from port 3 that is provided to the input ofthe horn antenna 5618 that provides a gain of the 20 dBi. A signalhaving a value of −42 dBm is transmitted from the horn antenna 5618through the window/wall 5606. The window/wall 5606 provides a 40 dB lossto the transmitted signal providing a −82 dBm signal at the receivinghorn antenna 5620. The horn antenna 5620 provides a further 20 dBi gainto the signal that is output at −62 dBm to the remaining circuitry ofthe inside portion 5608 of the device.

Referring now to FIG. 61, there is illustrated the signal strengths atvarious points of an uplink when no power amplifier is provided. Thetransmitted signals are provided at a strength of 18 dBm to the input ofthe horn antenna 5632. The horn antenna 5632 provides a gain of 20 dBito output a signal at 38 dBm through the window/wall 5606. Thewindow/wall 5606 causes a 40 dB loss to the signal such that thereceiving horn antenna 5638 receives a signal at −2 dB. The receivinghorn antenna 5638 boosts the signal to 18 dBm with a gain of 20 dBi. The18 dBm signal is input to port 1 of the circulator 5612. The circulator5612 causes a 2 dB loss to the signal which is output through port 2 at60 dBm. The transmitting antenna has a gain of 45 dB and a loss of twodB to cause a transmitted signal from the antenna at 59 dBm.

Referring now to FIG. 62, there is illustrated a further alternativeembodiment using a horn antenna is used for the transmission of signalsthrough the window or wall. As before, the millimeter wave transmissionsystem 5602 includes an exterior portion 5604 located on an exterior ofa window or wall 5606 and interior portion 5608 located on the interiorof the wall or window. The exterior portion 5604 includes an antenna5610 for transmitting and receiving signals to an exterior source.

The transmitted and received signals are processed at a 28 GHzcirculator 5612. The port 3 signals are provided to the input of a poweramplifier 5614. Similarly, the output of a power amplifier 5616 isconnected to input port 1 such that signals to be transmitted areprovided to port 2 of the circulator 5612 for transmission by antenna5610. The signals output from the power amplifier 5614 are provided to a28 GHz horn antenna 5618. The horn antenna 5618 transmitted to the RFsignals provided from the power amplifier 5614 through the window orwall 5606 to a receiving horn antenna 5620. The receive signals areoutput from the horn antenna 5620 to a modulator circuit 5622 fordemodulation. The demodulator 5622 in addition to receiving the receivesignal from for an antenna 5620 receives a signal output from a phaselocked loop/local oscillator 5624. The phase locked loop/localoscillator 5624 is controlled responsive to a clock generation circuit5626. The demodulated signal is provided from the demodulator 5622 toanalog-to-digital converter 5628. The digital signal is routed via arouter 5632 the appropriate receiving party.

Signals to be transmitted are received from inside the building at therouter 5630. In a one embodiment this will comprise a Wi-Fi router. Therouter 5630 provides digital signals to a digital to analog converter5632 converts the signals into an analogue format. The analog signalsare then modulated by a modulator 5634. The modulator 5634 modulates thesignals responsive to input from the phase locked loop/local oscillator5624 under control of the clock generation circuit 5626. The modulatedsignals from modulator 5634 are output through the window/wall 5606through a horn antenna 5636. The signals transmitted by horn antenna5636 or received by a receiving horn antenna 5638 located on theoutside. The output of the horn antenna 5638 is provided to the inputpower amplifier 5616 that amplifies the signal for transmission from theantenna 5610 after passing through circulator 5612.

The horn antennas 5618, 5620, 5636 and 5638 can have high gains of up to20 dB. The antenna patterns of these antennas will have side lobes andfront lobes. The front lobes are projected toward a receiving antenna.In order to shield the surrounding environment from emissions from theside lobes of the horn antennas 5618, 5620, 5636 and 5638, shielding6202 may be added over the horn antennas to provide adequate protectionto the environment in the vicinity of the device. The shielding 6202 actas absorbers to block the signals from the surrounding environment andmay comprise any material required to contain and absorb the emissionsof the horn antennas to a localized area contained within the shieldingenclosure 6202.

Referring now to FIG. 63, there is illustrated the manner in which powermay be provided to the external system component 6302 located within theexternal portion 5604 of the system and the internal system components6304 located within the internal portion 5608. The internal systemcomponent 6304 comprises the horn antennas 5620, 5636 modulator 5634,demodulator 5622 and other components discussed with respect to FIG. 56for generating signals for transmission and determining signals thathave been received. The external system components 6302 consist of thecirculator 5612, power amplifiers 5614, 5616 and horn antennas 5618,5638 described with respect to FIG. 56. The internal system component6304 are connected to an internal power system 6306 that may plug intothe electrical power system located within the building. Since theinternal system component 6304 and external system component 6302 areseparated by a window/wall 5606, there must be some manner fortransmitting or providing power to the external system components. Onemanner for doing so involves the use of a power system 6308 that ispowered by a number of solar panels 6310 that are located on theexterior of the building to which the external system component 6302 areconnected.

The power required from the power system 6308 to the external systemcomponents 6302 is approximately 0.76 W. One manner for providing this0.76 W power is through the use of solar panels 6310. Solar panelsproviding 0.76 W or 1 W may be utilized for the solar panels 6310. Withrespect to a 0.76 W power provision system, 0.76 W for 24 hours wouldrequire 18.24 W hours of power. If 18.24 W hours are provided at anefficiency of 1.25%, this will require 22.8 W hours. If an efficiency of22.8 W hours is divided by 3.5 hours (# number of daylight hours inwinter), a total result of 6.52 W is provided. Similarly for a 1 Wsystem, 1 W provided for 1 day requires 24 W hours. 24 W hours at a1.25% efficiency requires 30 W hours. 30 W hours divided by 3.5 hours ofsun available in the winter provides 8.57 W hours. The solar panels 6310used for providing power may be similar to those solar panels used forcharging smart phones and tablets. These type of panels include both 7 Wcharging panels and 9 W charging panels that meet the 0.76 W and 1 Wenergy levels requirements.

7 W portable solar chargers having high efficiency solar charging panelsnormally have a weight of 0.8 pounds. These devices have generaldimensions of 12.8×7.5×1.4 inches (32.5×19×3.5 cm). Other 7 W amorphoussolar power battery charger panels have a size of 15.8×12.5×0.8 inches(40×31.75×2 cm) and a weight of 3 pounds. Alternative 9 W chargingpanels with monocrystalline cells have dimensions ranging from8.7×10×0.2 inches (22×25.5×0.5 cm) and flexible solar panels have a sizeof 12×40 inches (30.5×100 cm). Other 9 W high-efficiency solar panelshave sizes from 8.8×12.2×0.2 inches (22.35×31×0.5 cm).

Referring now to FIG. 64, rather than utilizing solar panels, theexternal system components 6302 may utilize transmitted laser power forpowering the external system components rather than utilizing a solarpowered system. The internal system components 6304 have a power system6402 that provides power for all components on the interior portion of awindow or wall 6404. The power system 6402 has an internal powerconnection 6406 to for example, a power outlet located within thebuilding. The power system 6402 provides system power to the internalsystem components 6304 in a known manner. Additionally, the power system6402 provides power to a laser transmitter 6408. The laser transmitter6408 generates a laser beam 6410 that is transmitted through a window6404 to a photovoltaic receiver (PV receiver) 6412 located on theoutside of the window 6404. The laser transmitter 6408 includes a set ofoptics to define the beam size that is to be transmitted to the PVreceiver 6412. The generated laser power may be defined according to thefollowing equations:

$P_{Optic} = \frac{P_{Electric}}{{Eff}_{Optics} \times {{Eff}_{{PV}\mspace{11mu}{Cells}}(\eta)}}$${{QE}\left( {Eff}_{{PV} - {Cell}} \right)},{\eta = {{\frac{R_{\lambda}}{\lambda} \times \frac{hc}{e}} \approx {\frac{R_{\lambda}}{\lambda_{\mu\; m}} \times 1.24}}}$$\eta = {R\frac{1.24}{\lambda_{\mu\; m}}}$

The optical power needed by the PV receiver that detects energy at 445nm may be defined in the following manner:λ=445 nmThis is the wavelength of the receiver laser.

R = 0.25  (Hamamatsu  Si − photodiode)$\eta = {{R\frac{1.24}{\lambda_{\mu\; m}}} = 0.69}$Eff_(Optics) = 0.64  (Efficiency  of  Optics)$P_{Optic} = {\frac{P_{Electric}}{{Eff}_{Optics} \times {{Eff}_{{PV}\mspace{11mu}{Cells}}(\eta)}_{Optic}} = {\frac{0.76}{0.64 \times 0.69} = {1.72\mspace{14mu} W}}}$Thus, in order to provide power at 445 nm a 2 W laser diode is needed.The PV receiver 6412 converts received laser light energy back intoelectricity. Power generated by the PV receiver 6412 responsive to thereceived laser beam 6410 is provided to the power system 6414. The powersystem 6414 and provides power to the external system component 6302 toenable their operation.

Referring now to FIG. 65, there is illustrated a further manner forpowering exterior components from an interior power source usinginductive coupling rather than utilizing solar panels or a laser source,the external system components 6302 may utilize power provided byinductive coupling to the internal power source through the window/wall6504 for powering the external system components. The internal systemcomponents 6304 have a power system 6502 that provides power for allcomponents on the interior portion of a window or wall 6504. The powersystem 6502 has an internal power connection 6506 to for example, apower outlet located within the building. The power system 6502 providessystem power to the internal system components 6304 in a known manner.Additionally, the power system 6502 provides power to a inductive coil6508. The inductive coil 6508 enables a magnetic connection with asecond inductive coil 6512 located on the exterior of the window/wall6504. The inductive coils 6508 and 6512 enable the inductive coupling ofpower from the internal power system 6502 to the external power system6514. Power received at the inductive coil 6512 responsive to thereceived electromagnetic energy 6510 is provided to the power system6514. The power system 6514 and provides power to the external systemcomponent 6302 to enable their operation.

Also, in addition to the actively powered devices illustrated in FIGS.63, 64 and 65, a passively powered device may be used that provides nopowering to the exterior components but provides a shorter distance orhigher power from the internal components within the building.

The described system provides an optical or RF tunnel that allowssignals to be transmitted from outside a building to devices within thebuilding. The optical or RF tunnel can also be used to allow signalsfrom the Internet of Things devices located within the building to gofrom inside to outside. In addition to the techniques described hereinabove, other near field techniques can be used for transmitting theinformation through the window or wall.

It will be appreciated by those skilled in the art having the benefit ofthis disclosure that this regeneration and retransmission of millimeterwaves for building penetration provides a manner for providingmillimeter wave signals inside of a building where the signals do noteffectively penetrate. It should be understood that the drawings anddetailed description herein are to be regarded in an illustrative ratherthan a restrictive manner, and are not intended to be limiting to theparticular forms and examples disclosed. On the contrary, included areany further modifications, changes, rearrangements, substitutions,alternatives, design choices, and embodiments apparent to those ofordinary skill in the art, without departing from the spirit and scopehereof, as defined by the following claims. Thus, it is intended thatthe following claims be interpreted to embrace all such furthermodifications, changes, rearrangements, substitutions, alternatives,design choices, and embodiments.

What is claimed is:
 1. A system for enabling signal penetration into abuilding, comprising: first circuitry, located on an outside of thebuilding, for receiving millimeter wave signals and converting themillimeter wave signals into a format that overcomes losses caused bypenetrating into an interior of the building over a wirelesscommunications link, wherein the first circuitry further comprises: atleast one power amplifier for amplifying the received millimeter wavesignals to a level that counteracts losses occurring when the millimeterwave signals are transmitted from the outside of the building to theinterior of the building; and second circuitry, located on the interiorof the building and communicatively linked with the first circuitry viathe wireless communications link, for receiving the millimeter wavesignals in the format that overcomes the losses caused by penetratinginto the interior of the building and converting the millimeter wavesignals in the format to a second format for transmission to thewireless devices within the building.
 2. The system of claim 1 furthercomprising: wherein the first circuitry further comprises: an antennafor transmitting and receiving the millimeter wave signals; at least oneof a first conical or horn antennas for transmitting and receiving theamplified millimeter wave signal from/to the outside of the buildingto/from the interior of the building; wherein the second circuitryfurther comprises: at least one of a second conical or horn antennas forreceiving and transmitting the amplified millimeter wave signal from/tothe at least one first conical or horn antennas; and transceivercircuitry for converting the received, amplified millimeter wave signalto the second format for transmission to the wireless devices within thebuilding.
 3. The system of claim 1, wherein the at least one poweramplifier further amplifies millimeter wave signals before they aretransmitted by the at least one of the first canonical or horn antenna.4. The system of claim 1 further including at least one solar panelassociated with the at least one power amplifier, the at least one solarpanel providing power for operating the at least one power amplifier. 5.The system of claim 1 further including a laser power system forproviding power to the at least one power amplifier, the laser powersystem further comprising: a laser for generating a beam fortransmission of light energy from the interior of the building to theexterior of the building; and a photovoltaic receiver for receiving thelight energy from the laser beam and generating electrical energy topower the at least one power amplifier.
 6. The system of claim 1 furtherincluding an inductive coupling system for providing power to the atleast one power amplifier, the inductive coupling system furthercomprising: a first inductive coil located on the interior of thebuilding and connected to a power system located in the interior of thebuilding; and a second inductive coil located on the exterior of thebuilding and inductively coupled to the first inductive coil, the secondinductive coil connected to provide electrical energy to the at leastone power amplifier.
 7. The system of claim 2 further including a secondat least one power amplifier located on the interior of the building foramplifying the millimeter wave signals from the transceiver to a secondlevel that counteracts losses occurring when the millimeter wave signalsare transmitted from the interior of the building to the exterior of thebuilding.
 8. The system of claim 1 further including an RF circulatorfor interconnecting the antenna with the at least one power amplifier.9. The system of claim 2, wherein the first and second at least one ofthe conical or horn antennas have a gain of at least 20 dB.
 10. Thesystem of claim 2 further including a shielding material for limitingtransmissions that do not pass directly between the first at least oneconical or horn antenna and the second at least one conical or hornantenna.
 11. The system of claim 1, wherein the second circuitry furthercomprises a WiFi router to transmit signals in the format to thewireless devices within the building.
 12. The system of claim 1, whereinthe first circuitry and the second circuitry are communicatively coupledvia an RF tunnel.
 13. The system of claim 1, wherein the first circuitryand the second circuitry are communicatively coupled via a nearfieldtechnique.
 14. A system for enabling signal penetration into a building,comprising: first circuitry, located on an outside of the building, forreceiving millimeter wave signals and converting the millimeter wavesignals into a format that overcomes dB losses caused by penetratinginto an interior of the building over a wireless link, wherein the firstcircuitry further comprises: at least one power amplifier for amplifyingthe received millimeter wave signals to a level that counteracts dBlosses occurring when the millimeter wave signals are transmitted fromthe outside of the building to the interior of the building; secondcircuitry, located on the interior of the building and communicativelylinked with the first circuitry via the wireless link, for receiving themillimeter wave signals in the format that overcomes dB losses caused bypenetrating into the interior of the building and converting themillimeter wave signals in the format to a second format fortransmission to wireless devices within the building; and wherein thefirst circuitry and the second circuitry are communicatively coupled viaan RF tunnel.
 15. A system for enabling signal penetration into abuilding, comprising: first circuitry, located on an outside of thebuilding, for receiving millimeter wave signals and converting themillimeter wave signals into a format that overcomes dB losses caused bypenetrating into an interior of the building for reception by wirelessdevices within the building, wherein the first circuitry furthercomprises: an antenna for transmitting and receiving the millimeter wavesignals; at least one power amplifier for amplifying the receivedmillimeter wave signals to a level that counteracts the dB lossesoccurring when the millimeter wave signals are transmitted from outsidethe building to the interior of the building; transceiver circuitry fortransmitting and receiving the amplified millimeter wave signal from/tothe outside of the building to/from the interior of the building. 16.The system of claim 15, wherein the at least one power amplifier furtheramplifies millimeter wave signals before they are transmitted by thetransceiver circuitry.
 17. A system for enabling signal penetration intoa building, comprising: first circuitry, located on an outside of thebuilding, for receiving millimeter wave signals and converting themillimeter wave signals into a format that overcomes dB losses caused bypenetrating into an interior of the building for reception by wirelessdevices within the building, wherein the first circuitry furthercomprises: at least one power amplifier for amplifying the receivedmillimeter wave signals to a level that counteracts losses occurringwhen the millimeter wave signals are transmitted from the outside of thebuilding to the interior of the building; and second circuitry, locatedon the interior of the building and communicatively linked with thefirst circuitry, for receiving the millimeter wave signals in the formatthat overcomes the dB losses caused by penetrating into the interior ofthe building and converting the millimeter wave signals in the format toa second format for transmission to a wireless device within thebuilding.
 18. The system of claim 1, wherein the losses further includeat least one of absorption losses, scattering losses and reflectionlosses.
 19. The system of claim 14, wherein the dB losses furtherinclude at least one of absorption losses, scattering losses andreflection losses.
 20. The system of claim 15, wherein the dB lossesfurther include at least one of absorption losses, scattering losses andreflection losses.
 21. The system of claim 17, wherein the dB lossesfurther include at least one of absorption losses, scattering losses andreflection losses.